feat: Use uv package manager

[suejung-sentry]

Update api to use a more modern package manager (uv). This will let us more easily convert to monolith in the future.

Shared is getting converted in here: https://github.com/codecov/shared/pull/423 Worker is getting converted in here: https://github.com/codecov/worker/pull/896

Notable changes

• I moved over existing requirements.in 1:1 into new pyproject.toml to use uv-tools for build instead of pip-compile. Any deps that appeared to be used for dev only were added to dev-dependencies. The new lockfile will be uv.lock
• I updated the existing use of sentry-sdk[celery] to fix its build error. As long as we use CeleryIntegration, can remove the custom wrapping with _wrap_async
• Docker and Makefile stuff was updated to match that done for worker in above

Closes https://github.com/codecov/engineering-team/issues/2779