I don’t have any references and I’m not ATC, but this is what I’ve observed in Australia, which was an early adopter of mandatory ADSB for IFR in controlled airspace a few years ago:
Non-radar controlled enroute airspace with ADSB coverage (pretty much the whole country at airline cruise levels but not the whole ATC region) appears to operate similarly to radar airspace: No position reports, vectors available on request, separation standards similar to radar airspace. Some procedural separation standards may still apply to ADSB-exempt IFR, eg legacy military aircraft.
ADSB surveillance separation is not yet available in non-radar terminal airspace - procedural only. Although the tower controller can “see you” on a surveillance display, he can’t base separation on it or provide vectors.
It’s pretty awesome to be “identified” immediately on takeoff out of a Class G mining airstrip 1000 NM from the nearest civilisation. Australia has very limited radar coverage away from populated areas. So ADSB is a huge advancement here, hence the early adoption.
Observation only.