[chore] Move to Oxlint (#3384)

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# Why

We're moving to Oxc in universe too. The toolset is faster than ESLint / Prettier.

# How

Asked Codex to migrate the repository. I don't think all rules got migrated, unfortunately, but also the lint are in a bit weird state (different rules in `eas-cli` vs the rest of the repo). I hope we can unify the rules soon.

# Test Plan

CI should pass.