Investigate reason for `compute` not being released

[diegomarquezp]

Compute has not been released for a few months. The two main reasons are:

• The current generation workflow tries to push a commit directly via the GitHub API, which hits a commit size limit (compute is a very big library).
• Even if we manually create a pull request, the PR has compilation issues described in chore: regenerate compute clients #31255.

Next:

• In short term, solve the compilation issues before a manual push
• Long term, finish the implementation in build: [WIP] checkout and push instead of direct calls to GitHub API #31118