I also think it would be the responsibility of the person who want to merge their stuff. If it is a rebase or merge is unrelated

Why?

I experienced way too often that a feature branch worked perfectly fine, tests were successful etc. Then it is merged in main and there was a change in some code which the feature branch uses etc and it breaks.
To prevent this, get the branch to the latest state before merging, build it and run tests. Afterwards merge it.

Otherwise I don't know a better way to prevent breakage on main.