Add a minimal test on CI that `compile-commands.json` can be consumed by `clangd`

See https://github.com/flutter/flutter/issues/141640 for details.

Ideally we'd have a test, even just on Linux, that verifies that `clangd` can ingest `compile-commands.json` out of the box.