Thanks, I've investigated this and logged two separate bugs.
Studio is incorrectly treating Packages/objo.lock.json as being outside the solution, which explains both the missing commit entry and the warning in your screenshot. Plugin settings should be included. I've logged that here.
I've also reproduced the persistent MainMenuBar entry using Windows line endings. Studio sees a difference in the layout file's raw bytes, but Git normalises those line endings and finds nothing to commit. Studio then keeps showing the same item as modified. That closely matches what you're seeing, although I haven't confirmed your project's exact trigger. I've logged this separately here.
For now, you can use Fork to commit the plugin lock file. Both bugs are logged for fixing.