precompile: pipe error messages during autoprecompilation to Main.err for easier inspection

[IanButterworth]

It seems the way auto-precompilation only summarizes which packages errored not the verbose error details is unpopular so this makes autoprecompilation show errors the way an explicit Pkg.precompile does.

Updated: Now autoprecompilation pipes any errors to Main.err

Precompiling project...
  ✗ PNGFiles
  0 dependencies successfully precompiled in 1 seconds. 38 already precompiled.
  To see a full report use `julia> err`

julia> err
The following 1 direct dependency failed to precompile:

PNGFiles [f57f5aa1-a3ce-4bc8-8ab9-96f992907883]

Failed to precompile PNGFiles [f57f5aa1-a3ce-4bc8-8ab9-96f992907883] to "/Users/ian/.julia/compiled/v1.11/PNGFiles/jl_X0edfU".
ERROR: LoadError: 
Stacktrace:
 [1] error()
   @ Base ./error.jl:44
 [2] top-level scope
   @ ~/Documents/GitHub/PNGFiles.jl/src/PNGFiles.jl:3
 [3] include
   @ Base ./Base.jl:493 [inlined]
 [4] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::Nothing)
   @ Base ./loading.jl:2244
 [5] top-level scope
   @ stdin:3
in expression starting at /Users/ian/Documents/GitHub/PNGFiles.jl/src/PNGFiles.jl:1
in expression starting at stdin:3


julia> 

Also in noninteractive & CI modes it will always show errors now.

Closes #3444
Closes #3428

[staticfloat]

I have the following thoughts:

1. I'm not against hiding errors by default (although I do generally want to see them), but the command to see the errors seemed unnecessarily verbose. I don't like that I have to run import Pkg; Pkg.precompile() to see them; I just ran ]precompile, why should there be a difference between the two?
2. It would be nice if there were a way to interactively see the errors. Precompilation errors can be deceptively complex, and many times you end up chasing down 7 precompilation errors that are really one dependency deep in the stack that is failing and killing all dependent packages. My ideal interface would be to be able to view the errors that Pkg has already encountered through some kind of terminal menu, preferably topologically sorted to surface the deepest error first.
3. I think hiding errors is only acceptable if the errors can be easily viewed afterward. So even if the dream scenario of (2) is not implemented, perhaps writing the precompilation errors out to a temporary directory that gets cleaned up on Julia process exit, (or a scratch space that gets cleaned out on next precompile) would allow for better error analysis.

[IanButterworth]

It could be pushed to err, which would require making the error reports actual errors with show methods.

[IanButterworth]

But in no interactive mode it should just show

[IanButterworth]

Updated to use julia> err. See example up top

[IanButterworth]

@fredrikekre is there a reason why chaning this show method is bad, given #1080 ?

[IanButterworth]

I decided to make a new error type with a show method, given I guess there was a reason why this was tested for

[IanButterworth]

I'm going to merge and get this onto julia master so we can try it out before 1.10

[IanButterworth]

@KristofferC Maybe marking this for backport is too much? What do you think?