[ITensorsPackageCompilerExt] Superseding indictment of ITensorsPackageCompilerExt

[mtfishman]

This PR supersedes #1549 as a fix for #1548 (see also https://itensor.discourse.group/t/itensorspackagecompilerext-precompilation-failure-julia-v1-11/2070).

Closes #1548 and closes #1549 (@kmp5VT).

I noticed that ITensorsPackageCompilerExt was erroneously including and running the compilation script when it is loaded, so that it was actually running ITensor code (such as DMRG) when it was being loaded, while that script should only be run if a user wants to compile ITensor code into a system image.

I don't know why that workflow was ok in Julia 1.10 and below but causes problems during precompilation in Julia 1.11. My only guess is that in Julia 1.11 there was a change to the ordering of when package extension code gets loaded and/or precompiled. Anyway, I'm not sure it is worth investigating since a more sane workflow seems to work without any problems.

I also added a somewhat crude test that checks that ITensors.compile gets overloaded when ITensorsPackageCompilerExt gets loaded. This test would have caught the original issue since the test file would have failed when trying to load ITensorsPackageCompilerExt in the first place.