Convert julia-repl blocks to jldoctest format

[Keno]

Convert appropriate julia-repl code blocks to jldoctest format to enable
automatic testing. In addition, this introduces a new nodoctest = "reason"
pattern to annotate code blocks that are deliberate not doctested, so future
readers will know not to try.

Many code blocks are converted, in particular:

• Manual pages: arrays.md, asynchronous-programming.md, functions.md,
  integers-and-floating-point-numbers.md, metaprogramming.md,
  multi-threading.md, performance-tips.md, variables.md,
  variables-and-scoping.md
• Base documentation: abstractarray.jl, bitarray.jl, expr.jl, file.jl,
  float.jl, iddict.jl, path.jl, scopedvalues.md, sort.md
• Standard library: Dates/conversions.jl, Random/RNGs.jl,
  Sockets/addrinfo.jl

Key changes:

• Add filters for non-deterministic output (timing, paths, memory addresses)
• Add setup/teardown for filesystem operations
• Fix parentmodule(M) usage in expr.jl for doctest compatibility
• Document double escaping requirement for regex filters in docstrings
• Update AGENTS.md with test running instructions

Note: Some julia-repl blocks were intentionally left unchanged when they
demonstrate language internals subject to change or contain
non-deterministic output that cannot be properly filtered.

Refs #56921

[Keno]

This has been mostly written by various AI agents - it's been a bit of my go to test case. All of them struggle with this quite a bit. However, I do think the changes are useful and I'm mostly out of patience with the AI agents, so this is the rollup of the useful changes.

[Keno]

Should have carried state from the definition above

[fingolfin]

so... we should give this block a label, and change the preceding block defining f to also use that label (and presumably turn it into a jldoctest block for that as well... ?

I.e. like this (I cannot post this as a code change comment here because the block above is "out of range")

For example, in the function
```jldoctest argpassing; output = false
function f(x, y)
    x[1] = 42    # mutates x
    y = 7 + y    # new binding for y, no mutation
    return y
end

# output
(generic function with 1 method)
```
The statement .... blah ...
```jldoctest argpassing
julia> a = [4, 5, 6]
...
```

[fingolfin]

Looks good to me and definitely a move in the right direction :-)

[Keno]

Should be a filtered jldoctest

[Keno]

Iteration order depends on hashes for IdDict. Needs a filter that accept any RHS/LHS of the =>