Removes the legacy analysis options override and fixes all resulting issues. This is a combination of dart fix and manual changes (mostly mechanical, but some small restructuring to address warnings more cleanly, such as creating typed structs from args when they are used repeatedly to avoid repeated casting, or making things that were unnecessarily public private).
One small opportunistic extra cleanup is that the handling of null-safety prerelease versions is removed, as any new plugin would be written null-safe from the start, so we no longer need to allow those versions.
Part of flutter/flutter#76229
