Manually make Cursor Tab suggest code

Continuing the discussion from Manually make Cursor Tab suggest code?:

Similarly to how one can trigger suggestions from the language server (Ctrl+Space on Windows, some weird binding on MacOS), there should be a command for requesting Cursor Tab autocompletion.

My main use case: When searching with Ctrl+F, I see precisely the autocomplete I want, I press Esc to exit search and now my precious suggestion is gone!