GH-48594: [C++][FlightRPC] Fix ODBC CI Long Build Time Issue

[alinaliBQ]

Rationale for this change

#48594

What changes are included in this PR?

• Resolve caching issue inside ODBC CI, so build time is generally less than 1hr
• Removed environment variables that are not necessary for ODBC building to keep workflow simple

Are these changes tested?

• Tested in CI

Are there any user-facing changes?

N/A

• GitHub Issue: [C++][FlightSQL][ODBC] MSVC CI caching issues #48594

[github-actions]

⚠️ GitHub issue #48594 has been automatically assigned in GitHub to PR creator.

[alinaliBQ]

Hi @pitrou and @raulcd, to follow up on #48313 I have opened this draft PR.

As Raul has pointed out in #48313 (comment), there is an issue pushing the packages to nuget. Therefore, when a new ODBC build begins, all vcpkg packages are rebuilt and that is the root cause of the long ODBC build time.

Does it require any changes in the GitHub repository settings to allow the new workflow to push packages to https://nuget.pkg.github.com/apache?

[alinaliBQ]

During investigation, I tried running vcpkg install command before the cpp_build.sh script in C GLib & Ruby MSVC workflow, and it has the same 403 error as ODBC MSVC. But the script cpp_build.sh in GLib workflow can still publish nuget packages normally. I am not sure why the same script works in GLib MSVC, but not in ODBC MSVC.
Run log: https://github.com/apache/arrow/actions/runs/20353354024/job/58483242851?pr=48595#step:13:3353

[alinaliBQ]

ODBC build time has been reduced to around 40 - 60 mins. PR is ready for review. Raised an issue for the flakey 403 request error #48604. Raised #48606 for nuget push timeout issue.