For playing in the World Championship, it is "passport holder", I believe. There is the problem of dual citizenship and that would be where the time between changes would come in. Some organizations have a five-year (maybe three?) transition period without playing.
I think Matchroom is free to do as they please and maybe someone switching sides would be an interesting wrinkle. It would be really strange for Shaw to switch. Fedor would seem a lot more neutral.
On the Joe Rogan show he said something to the effect that he'd need to sit out three years of events to change the nationality he represents.
It's interesting because the rule actually comes from the Olympic Charter (Page 77, Rule 41, Bye-law 2). The rule is that three years must pass since he last represented his old country before he may represent his new country.
https://stillmed.olympic.org/.../EN-Olympic-Charter.pdf
So questions arise like first does that only apply to the Olympic Games (or World Games?) themselves and might the WPA be inclined to use that as a guideline for their own rulings but do they actually have some discretion regarding the handling of general international competition?
And second, when was the last time Fedor represented Russia in international competition? With the bans and him now competing unaffiliated, it may be the case the three years are nearly lapsed already provided he doesn't represent Russia in any future event and reset the clock.
It may be the case he could be good to go as soon as his citizenship clears if he works with the WPA and plays his cards right.
And ultimately the relationship between Matchroom and WPA also makes you wonder whether those IOC-oriented protocols will mean anything to Matchroom running non-sanctioned invitational events that don't award federation-recognized medals.