[WIP] Add datatype, in-place one!/unmatricize!, make scalar/similar_map public

[mtfishman]

Summary

Small additive utilities on the tensor-algebra interface.

datatype(a) returns the underlying storage array type, the element type together with the container/device (e.g. Matrix{Float64}), complementing scalartype/eltype, which give the element type alone. It recurses through array wrappers via parent and terminates on a plain array, with a type-level base case datatype(::Type{<:AbstractArray}). scalar and similar_map become public.

one!(A, ndims_codomain::Val) fills A in place with the identity across a codomain/domain split and returns it. It matricizes, fills the fused matrix, and scatters back only when the matricized form is a detached copy (a graded gather) rather than a view aliasing A (a dense reshape). unmatricize!(a_dest, m, ndims_codomain::Val) scatters a fused matrix back into an existing array, the split-axes counterpart of unmatricizeperm!.

svd_trunc now returns the truncation error ϵ, the 2-norm of the discarded singular values, as a fourth output, so callers get it cheaply and without catastrophic cancellation instead of recomputing it from norms.

TODO

• Exercise the new API from the downstream migration before marking ready.

[codecov]

Codecov Report

❌ Patch coverage is 95.83333% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 76.94%. Comparing base (8567e35) to head (d32f1be).

Files with missing lines	Patch %	Lines
src/factorizations.jl	92.85%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #205      +/-   ##
==========================================
- Coverage   80.32%   76.94%   -3.38%     
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  Files          23       23              
  Lines         869      885      +16     
==========================================
- Hits          698      681      -17     
- Misses        171      204      +33     

Flag	Coverage Δ
docs	22.24% <16.66%> (-0.16%)	⬇️

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