Is that just for the connection phase? Or does it then start publicly broadcasting a persistent MAC onced it's connected, so if you earbuds or watch are connected and communicating with your phoine, would a sniffer see a persisten MAC address or the session randomised one?

That's a problam (one of many problems) with WiFi MAC address randomisation - you can sniff the network names a phone is trying to connect to, then stand up a wifi access point with one of those names and the phone will reveal its real MAC address when it connects. I experimented a long time back with having a raspi that broadcast itself as a McDonalds free wifi access point, a huge number of phones would try to connect while I was out in public with it.