Use Base.require() to load Distributed internally (#54571)

TL;DR: we changed to loading stdlibs exclusively from the default sysimg
in JuliaLang/julia#53326, and this breaks
developing Distributed.jl because the workers will load the builtin
version instead of the development version. I think this should be
backported to 1.11?

CC @jpsamaroo

---

`Base.require_stdlib()` will exclusively load a stdlib from whatever was
shipped with Julia. The problem is that when developing Distributed.jl
this will cause the workers to always load the builtin Distributed
module instead of the development version, which can break everything
because now the master and worker are running different (potentially
incompatible) versions of Distributed.

This commit changes Base and LinearAlgebra to use `Base.require()`
instead, which will respect `Base.LOAD_PATH`. I argue that this is safe
because unlike the other stdlibs like REPL or Pkg, Distributed is only
loaded if explicitly requested by the user with `-p` or through
`addprocs()` or something, so it shouldn't be possible to get into quite
the same
tools-are-broken-because-I-broke-my-tools situation that motivated using
`Base.require_stdlib()` in the first place.

An alternative design would be to:
1. Move the if-block loading Distributed in `exec_options()` below the
for-loop where it will execute `-e` options.
2. Require any implementation of `Distributed.launch(::ClusterManager)`
to pass `-e 'using Distributed'` in their command to ensure that
Distributed is loaded in a way respecting `Base.LOAD_PATH`.

This would be more consistent with how the other stdlibs must be
developed, but it requires implementers (i.e. Distributed and
ClusterManagers.jl) to opt-in to allowing development versions of
Distributed, which feels very annoying and easy to miss so I decided not
to implement that.

(cherry picked from commit 3b922b0a129e89b5fed0045f20f51f3c16a75079)
(cherry picked from commit af49d9f1c2eb917628ca47d29f5ffbef79463101)

src/LinearAlgebra.jl

@@ -717,7 +717,7 @@ function peakflops(n::Integer=4096; eltype::DataType=Float64, ntrials::Integer=3
     end
 
     if parallel
-        let Distributed = Base.require_stdlib(Base.PkgId(
+        let Distributed = Base.require(Base.PkgId(
                 Base.UUID((0x8ba89e20_285c_5b6f, 0x9357_94700520ee1b)), "Distributed"))
             nworkers = @invokelatest Distributed.nworkers()
             results = @invokelatest Distributed.pmap(peakflops, fill(n, nworkers))