Yes, Home Screen apps don't have this limitation, here are the official docs: https://webkit.org/tracking-prevention/#intelligent-tracking-prevention-itp
As for the persistence permission: there is no official info on whether this is "stronger" than ITP (apart from a Twitter thread at /firt/status/1592326461050204160), but our experience is that it does protect data from being deleted. However, as you mentioned, it has to be requested every time your app is opened.