Precompilation issues with `detect_ambiguities` and `test_stale_deps`

[luke-kiernan]

In PowerNetworkMatrices, we currently have a situation where aqua tests error. If I run test_ambiguities, I get:

ERROR: LoadError: Failed to parse output of `detect_ambiguities`. 

The stdout was:

The stderr was: Precompiling packages...
Info: Given PowerNetworkMatrices was explicitly requested, output will be shown live
ERROR: LoadError: UndefVarError: `AAFactorization` not defined in `AppleAccelerate`
Suggestion: check for spelling errors or missing imports.

Yet if I locally run using AppleAccelerate, then AppleAccelerate.AAFactorization is just fine.
If I run test_stale_deps, I get something even stranger:

ERROR: LoadError: failed process: Process(`/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/bin/julia -C native -J/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/lib/julia/sys.dylib -g1 --startup-file=no --color=no -e 'append!(empty!(Base.DEPOT_PATH), ["/Users/me/.julia", "/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/local/share/julia", "/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/share/julia"])
append!(empty!(Base.DL_LOAD_PATH), ["/Users/me/Documents/julia/Sienna/psy5/PowerNetworkMatrices.jl/@loader_path"])
append!(empty!(Base.LOAD_PATH), ["/Users/me/Documents/julia/Sienna/psy5/PowerNetworkMatrices.jl/test/Project.toml", "/Users/me/.julia/environments/v1.12/Project.toml", "/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/share/julia/stdlib/v1.12"])
ENV["JULIA_LOAD_PATH"] = "/Users/me/Documents/julia/Sienna/psy5/PowerNetworkMatrices.jl/test/Project.toml:/Users/me/.julia/environments/v1.12/Project.toml:/Users/me/.julia/juliaup/julia-1.12.1+0.aarch64.apple.darwin14/share/julia/stdlib/v1.12"
Base.set_active_project(nothing)

Base.require(Base.PkgId(Base.UUID(0xbed98974b02a5e2f9fe0a103f5c450dd), "PowerNetworkMatrices"))
print("_START_MARKER_")
for pkg in keys(Base.loaded_modules)
    pkg.uuid === nothing || println(pkg.uuid)
end
'`, ProcessExited(1)) [1]

Stacktrace:
  [1] pipeline_error
    @ ./process.jl:598 [inlined]
  [2] read(cmd::Cmd)
    @ Base ./process.jl:482
  [3] read
    @ ./process.jl:491 [inlined]
  [4] find_stale_deps(pkg::Base.PkgId; ignore::Vector{Symbol})
    @ Aqua ~/.julia/packages/Aqua/MCcFg/src/stale_deps.jl:64
  [5] find_stale_deps
    @ ~/.julia/packages/Aqua/MCcFg/src/stale_deps.jl:45 [inlined]
  [6] test_stale_deps(pkg::Base.PkgId; kwargs::@Kwargs{ignore::Vector{Symbol}})
    @ Aqua ~/.julia/packages/Aqua/MCcFg/src/stale_deps.jl:30
  [7] test_stale_deps
    @ ~/.julia/packages/Aqua/MCcFg/src/stale_deps.jl:29 [inlined]
  [8] #test_stale_deps#26
    @ ~/.julia/packages/Aqua/MCcFg/src/stale_deps.jl:35 [inlined]
  [9] top-level scope
    @ ~/Documents/julia/Sienna/psy5/PowerNetworkMatrices.jl/test/runtests.jl:29
 [10] include(mapexpr::Function, mod::Module, _path::String)
    @ Base ./Base.jl:307
 [11] top-level scope
    @ REPL[11]:1

ChatGPT suggests it's something with how Aqua is launching a new Julia process using the current binary, and setting up its own environment variables. That somehow leads to re-precompilation of AppleAccelerate under a slightly different context, but reusing the old cache.