Change bencher CI to use commit checks

[teofr]

No description provided.

[changeset-bot]

⚠️ No Changeset found

Latest commit: 8d8dc14

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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[teofr]

Closing since bencher doesn't allow it. Tracking on bencherdev/bencher#894