Backport FPS polling fix to 1.16.X branch

[Ricket]

• Cherry-picked the main commit e9ee15b6c25af5ae962bbbaafdf33e75c13dc07a , fixed 1.19->1.16 differences, and then manually applied two followup commits (part of 7e89132e1839098bbb01cdf247967484709abf27 , and 9172ddb6e8c078c9e60e2fe845a4df267e3b2cd0 ).
• Tested briefly via just running from IntelliJ; controller button presses seem responsive at all framerate limits.
• Note I removed the index parameter from the @ModifyVariable annotation, because the 1.19 value of 7 didn't work and I wasn't sure how to determine it. The docs say that if you omit index, it will just apply to all matches, which certainly is fine in this case since there's only one invocation.

[Ricket]

The mixin fails when used on 1.16.5 with Forge 1.16.5-36.2.39. I'm making my own personal fixes and builds tailored specifically to my modpack and not making an effort to test or generalize them so I'll just close this PR.