docs: update/cleanup Invite documentation

[shiftinv]

Summary

Fixes backticks, adds missing Optional[] types, and adds links back to the table explaining the conditions under which attributes exist.

Checklist

• If code changes were made, then they have been tested
  • I have updated the documentation to reflect the changes
  • I have formatted the code properly by running task lint
  • I have type-checked the code by running task pyright
• This PR fixes an issue
• This PR adds something new (e.g. new method or parameters)
• This PR is a breaking change (e.g. methods or parameters removed/renamed)
• This PR is not a code change (e.g. documentation, README, ...)