"Race condition" between opening a newdle, people responding and updating its participants

According to a ticket we just got, there's most likely a bug where a participant can be silently lost:

1. Creator keeps their newdle (summary page) open in the browser
2. Someone who is not yet a participant responds to the newdle -> new participant is created
3. Creator edits the newdle's participants (e.g. removing or adding someone)

Most likely any participant that was created between step 1 and 3 is removed by [this code](https://github.com/indico/newdle/blob/master/newdle/api.py#L379-L392).

The best solution would probably be to not actually remove participants from the list when sending the PATCH request but rather setting something like `deleted: true`, and then only removing participants for which we received that data in the PATCH, and ignoring any participant that's simply not in the list.

Note: I have not tried to reproduce the issue, but it's the only logical explanation and the server logs for the newdle from the ticket don't contradict this.

Start in newdle/api.py around lines 379-392 and inspect how the PATCH request updates the participant list. Try to reproduce the reported sequence, or add coverage for a participant created between opening the summary and submitting the edit. Done means such a participant is not silently removed when the creator updates participants.

Written by the indexing model from the issue text.