Per https://github.com/eslint/rfcs/pull/127/changes#diff-7c99be846e07d8842a67527bcd47eb3175446759ac12beb6db87ac712a00a1f9R139-R141, the intended steps to roll out the ecosystem tests are:

1. On a CI cron job once a day, targeting the main branch but not blocking its builds
2. On the main branch only, with failures showing as failures in its builds
3. On all PRs targeting the main branch, alongside existing CI jobs

#19643 added step 1. Filing this issue to track step 2. The next step after this will be step 3.

Note that this is initially blocked on #20817's mentioned failures.