Unfortunately, updating the row also creates dead tuples. It's very tricky!
In this case, you might have enough dead tuples across your heap that you might get a lot of HOT updates. If you are processing in insertion order, you will also probably process in heap order, and you can actually get 0 HOT updates since the other tuples in the page aren't fully dead yet. You could try using a lower fillfactor to avoid this, but that's also bad for performance so it might not help.
As of PG16, HOT updates are tolerated against summarizing indexes, such as BRIN.
https://www.postgresql.org/docs/16/storage-hot.html
Besides, you probably don't want "done" jobs in the same table as pending or retriable jobs - as you scale up, you likely want to archive them as it provides various operational advantages, at no cost.
If you read my earlier comment properly, you'll notice a "done" column is to avoid deleting columns on the hot path and avoid dead tuples messing up the planner. I agree that a table should not contain done jobs, but then you risk running into the dead tuple problem. Both approaches are a compromise.