Preserved 47580 (Stratford 47 Group), D1755/47773 (Vintage Trains) and 47798 (NRM) are all mainline certified.
Correct, although only 773 sees any regular meaningful work on the mainline.
798 hasn't regularly done much since about 2012 ish when it had sanctions put on where and when it could be used after political interference from outside parties, as I know all too well when it was made unavailable the following year leaving a steam charter stuck in York most of the evening.
580 (of which I'm a shareholder) "might" see little or no further mainline use now as the wheels are on their final turn at the lathe and there isn't currently the support at the top of the group to sanction releasing a big chunk of our finances to order and purchase another set. Had we not had to carry out major generator repairs after its first major mechanical failure in preservation (and over a decade of being regarded as the most reliable member of its class left) in 2018, if I have my dates right, then I'm in little doubt it'd have moved onto new wheels by now and you'd still be seeing it as part of dual braked WCR pool as required.
As a footnote, we also have 47367 + 47596 which have to be kept going out of the same (dwindling) source of finances and with limited manpower to maintain them. All or some of our 3 47s would be put at risk longer term if the money all went into 580, although its entirely possible we won't be able to keep all 3 beyond the short to medium term if events dictated that it's no longer viable.