Make completions menu stay open after after it's manually requested (#32015)

Also includes a clarity refactoring to remove
`ignore_completion_provider`.

Closes #15549

Release Notes:

- Fixed completions menu closing on typing after being requested while
`show_completions_on_input: false`.
8c46a4f594Michael Sloan committed on 6/3/2025, 8:33:52 PM· committed by GitHubparent522abe8
7 files changedLine totals unavailable