Follow-up of https://github.com/zed-industries/zed/pull/29706

Instead of doing `cargo check` manually, use rust-analyzer's flycheck:
at the cost of more sophisticated check command configuration, we keep
much less code in Zed, and get a proper progress report.

User-facing UI does not change except `diagnostics_fetch_command` and
`env` settings removed from the diagnostics settings.

Release Notes:

- N/A