Add cargo udeps as a new CI check

[dimartiro]

Description

This PR removes unused dependencies, marks some others to be ignored, and introduces a cargo-udeps check in CI to prevent regressions.

It finalizes my work started in #9235, ensuring all unnecessary dependencies are cleaned up across the project.

Note: Since there are well known false positives I've checked each one and ignore the ones that we are 100% are false positives

Closes: #6906

[bkchr]

I'm not convinced to add this, there seems to be a lot of false positives that you need to handle.

[dimartiro]

I see your point. I think the false positives would be a real problem if we had no way to deal with them. But since we can safely ignore them, I believe it’s still a useful check

[bkchr]

But it clutters the Cargo.toml files.

[dimartiro]

IMO the trade-off is worth it — just a few extra lines to prevent unused dependencies, which would otherwise lead to bigger binaries and longer compilation times

[franciscoaguirre]

For me, the trade-off of having to ignore false positives in exchange for less useless dependencies is worth it

[dimartiro]

Updated based on the latest changes and unused deps