type promotion bug with parameter dependent `initialization_eqs`

**Describe the bug 🐞**

If a parameter changes its type (e.g. becomes a dual number) via `setsym_oop` and we need parameters in `initialization_eqs`, then the initialization problem does not correctly promote the type of `prob.f.initialization_data.initializeprob.f.resid_prototype`, leading to
```
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{:tag, Float64}, Float64, 1})
```
during initialization.

**Expected behavior**

The tests below should pass.

**Minimal Reproducible Example 👇**

```julia
@testset "type promotion with parameter dependent initialization_eqs" begin
    @variables x(t)=1 y(t)=1
    @parameters a=1
    @named sys = ODESystem([D(x) ~ 0, D(y)~x+a], t; initialization_eqs = [y ~ a])

    ssys = structural_simplify(sys)
    prob = ODEProblem(ssys, [], (0, 1), [])

    @test SciMLBase.successful_retcode(solve(prob))

    seta = setsym_oop(prob, [a])
    (newu0, newp) = seta(prob, ForwardDiff.Dual{ForwardDiff.Tag{:tag, Float64}}.([1.0], 1))
    newprob = remake(prob, u0=newu0, p=newp)

    @test SciMLBase.successful_retcode(solve(newprob))
end
```

**Error & Stacktrace ⚠️**

```julia
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{:tag, Float64}, Float64, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::UInt8)
   @ Base float.jl:245
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{:tag, Float64}, Float64, 1})
    @ Base ./number.jl:7
  [2] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{:tag, Float64}, Float64, 1}, i::Int64)
    @ Base ./array.jl:976
  [3] macro expansion
    @ ~/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:430 [inlined]
  [4] macro expansion
    @ ~/.julia/packages/Symbolics/YbNrd/src/build_function.jl:546 [inlined]
  [5] macro expansion
    @ ~/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:387 [inlined]
  [6] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/M9ZX8/src/RuntimeGeneratedFunctions.jl:163 [inlined]
  [7] macro expansion
    @ ./none:0 [inlined]
  [8] generated_callfunc
    @ ./none:0 [inlined]
  [9] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Nothing, ::Vector{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/M9ZX8/src/RuntimeGeneratedFunctions.jl:150
 [10] (::ModelingToolkit.var"#f#749"{…})(du::Vector{…}, u::Nothing, p::MTKParameters{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/0O7FS/src/systems/nonlinear/nonlinearsystem.jl:320
 [11] (::NonlinearFunction{…})(::Vector{…}, ::Vararg{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/VAClc/src/scimlfunctions.jl:2359
 [12] build_null_solution(prob::NonlinearLeastSquaresProblem{…}, args::Nothing; abstol::Float64, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:729
 [13] solve_call(_prob::NonlinearLeastSquaresProblem{…}, args::Nothing; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:624
 [14] solve_up(prob::NonlinearLeastSquaresProblem{…}, sensealg::Nothing, u0::Nothing, p::MTKParameters{…}, args::Nothing; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1105
 [15] solve(prob::NonlinearLeastSquaresProblem{…}, args::Nothing; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1036
 [16] get_initial_values(prob::ODEProblem{…}, valp::OrdinaryDiffEqCore.ODEIntegrator{…}, f::Function, alg::SciMLBase.OverrideInit{…}, iip::Val{…}; nlsolve_alg::Nothing, abstol::Float64, reltol::Float64, kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/VAClc/src/initialization.jl:209
 [17] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::SciMLBase.OverrideInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/initialize_dae.jl:159
 [18] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::OrdinaryDiffEqCore.DefaultInit, x::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/initialize_dae.jl:50
 [19] initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, initializealg::OrdinaryDiffEqCore.DefaultInit)
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/initialize_dae.jl:40
 [20] __init(prob::ODEProblem{…}, alg::OrdinaryDiffEqCore.CompositeAlgorithm{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Nothing, reltol::Nothing, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/solve.jl:514
 [21] __init (repeats 5 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/solve.jl:11 [inlined]
 [22] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/solve.jl:6 [inlined]
 [23] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/gALQU/src/solve.jl:1 [inlined]
 [24] solve_call(_prob::ODEProblem{…}, args::OrdinaryDiffEqCore.CompositeAlgorithm{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:632
 [25] solve_call
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:589 [inlined]
 [26] #solve_up#53
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1120 [inlined]
 [27] solve_up
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1099 [inlined]
 [28] #solve#51
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1036 [inlined]
 [29] solve
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1026 [inlined]
 [30] #__solve#3
    @ ~/.julia/packages/OrdinaryDiffEqDefault/2qVWT/src/default_alg.jl:46 [inlined]
 [31] __solve
    @ ~/.julia/packages/OrdinaryDiffEqDefault/2qVWT/src/default_alg.jl:45 [inlined]
 [32] #__solve#72
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1436 [inlined]
 [33] __solve
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1427 [inlined]
 [34] #solve_call#44
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:632 [inlined]
 [35] solve_call(::ODEProblem{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:589
 [36] solve_up(::ODEProblem{…}, ::Nothing, ::Vector{…}, ::MTKParameters{…}; kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1105
 [37] solve_up
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1099 [inlined]
 [38] solve(::ODEProblem{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1036
 [39] solve(::ODEProblem{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1026
 [40] top-level scope
    @ REPL[98]:1
Some type information was truncated. Use `show(err)` to see complete types.
```

**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia
Status `~/juliasim/dev/Project.toml`
  [2b5f629d] DiffEqBase v6.160.0
  [961ee093] ModelingToolkit v9.54.0
```

  - Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`

```julia

```

  - Output of `versioninfo()`

```julia
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × Intel(R) Core(TM) i9-14900K
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 32 default, 0 interactive, 16 GC (on 32 virtual cores)
```

**Additional context**

Add any other context about the problem here.


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type promotion bug with parameter dependent `initialization_eqs` #3246

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type promotion bug with parameter dependent initialization_eqs #3246

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type promotion bug with parameter dependent `initialization_eqs` #3246