Add CI check to oats

Oats has a test suite that only runs on publish, not on merge. We should set it up so that it runs before merging to master.

The issue names Oats's test suite and its current publish-time trigger, but no files or test command. Start by locating the publish workflow and test entry point, then verify how tests are invoked. Done means the suite runs successfully as a required check before merging to master.

Written by the indexing model from the issue text.