Respect `--output-format` with `--watch` (#21097)
Summary
--
Fixes #19550
This PR copies our non-watch diagnostic rendering code into
`Printer::write_continuously` in preview mode, allowing it to use
whatever output format is passed in.
I initially marked this as also fixing #19552, but I guess that's not
true currently but will be true once this is stabilized and we can
remove the warning.
Test Plan
--
Existing tests, but I don't think we have any `watch` tests, so some
manual testing as well. The default with just `ruff check --watch` is
still `concise`, adding just `--preview` still gives the `full` output,
and then specifying any other output format works, with JSON as one
example:
<img width="695" height="719" alt="Screenshot 2025-10-27 at 9 21 41 AM"
src="https://github.com/user-attachments/assets/98957911-d216-4fc4-8b6c-22c56c963b3f"
/>
