There is no such plugin. Someone would need to write it.
No. The plugin would do that. And it’s likely that there’s a way to discern when they got added via the database and data explorer, though I’m not really sure.
If you’re not self hosted, or for other reason don’t want a plugin,
It might also be possible to hack something together using the data explorer plugin (to get data on when they were added and hence, should be deleted) and use an automation/api tool (like zapier, though I’ve also used github actions) to remove them from the group when the time comes.