[infra] The breaking-change health bot is broken with workspaces

[dcharkes]

It looks like the dart_apitool may have trouble with native_toolchain_c being part of a pub workspace. It seems to be checking out the previous version of the package from pub and analyzing that code outside of its workspace, which seems to result in some problems. If I actually check out the whole repository at the old version's revision and have the tool compare that with the current revision, it correctly detects no breaking change: No breaking changes!

Originally posted by @goderbauer in #2347 (comment)

We should see if we can fix this. The check is useless for us otherwise.