My previous comment might have not been accurate. Some comments at meta suggest that Private Relay egress ranges could be not exclusively used by Private Relay. We'd need to confirm if that's the case or not.

To what extent could we specify that a message only be shown to people who are accessing Wikipedia through an IP proxy that is known to be blocked and associated with Apple's iCloud Private Relay Service?

Thanks for the update @AntiCompositeNumber. I have posted some thoughts at https://meta.wikimedia.org/wiki/Talk:Apple_iCloud_Private_Relay
but before this is announced more widely, I think it should be improved. For example, it should talk about affected editors, not blocked editors. No editor is blocked here, they are affected by an IP block under some circumstances, and there are many ways for them to continue editing (some have been discussed above in this ticket).

@Mess Workaround for stuck queries:

• Click Stop
• The button turns into Start query button for a fraction of second, before the alert error is shown, just click it before the error shows up.

I'm experiencing the same issue with enwiki_p. I have one job stuck in "running", another stuck in "queued", and stop button gives error 500 for both of them.

You should look at Spur. We are using it at the WikiProject on open proxies with very good results. I have independently verified its accuracy for many cases, and it is far superior to every option that has been mentioned in previous discussions.

A less intrusive alternative could be adding a new (optional) parameter to the extended image syntax to force a file to be sourced locally or from Commons.