In this design there is a new GHA job merged into the main repo that adds check runs to each PR on whether they have a silent merge conflict or not.
The idea is that we have a job that pretty much runs 24/7 triggered every 6 hours or so and set to run for 5.5 hours, it could be set to run on a GHA runner rather than a Cirrus runner. Obviously running on a Cirrus runner (or even multiple runners) would dramatically speed up how many PRs can be checked for silent merge conflicts.
The job uses the Github checks API to add a passing or failing test run to each PR directly. The silent merge check job itself should always pass, it writes pass or fail checks to the PRs.
It will look through all open PRs and discard anything that has a git merge failure or a failing test with the thinking that there is no point checking something that can't be merged anyway. Then it will select PRs that have not had a silent merge check and one by one pull the merge branch of the PR and the full CI job "Previous releases" on that branch.
When all PRs have been checked it will then re-check a PR that was checked the longest time ago.