I would imagine its too early to say TBT. Who knows how many other clubs may be in financial difficulties & may end up relegated.
IMO if Wasps do get relegated they may not survive at all.
What we know as Wasps now may not survive but I think Wasps is more than location based team, its an idea embodied by the phrase: Once a Wasp, always a Wasp. It is not London Wasps, Wycombe Wasps or even Worcester Wasps, it is just Wasps.
If it gets relegated out of its current existence I'm sure some group of fans and players will pick up the pieces and start again at the lowest level needed. Perhaps playing at Primrose Hill or Merchant Taylors (I've played cricket there, lovely setting) as an invitational team, initially.
No need for anyone to pick up the pieces and start again at the lowest level.
As RogerE says, the original Wasps club still exists, together with all those intangibles you mention and over 150 years of history. The professional outfit broke away in 1996 and the 2 clubs have continued to operate with that shared history and heritage. If the pro team goes to the wall, then we will be back to just one.
Currently playing in Counties 2 Herts/Middx (8th tier).
https://www.englandrugby.com/fixtures-and-results/search-results?competition=261&division=39116&season=2022-2023#fixturesHome games at Twyford Avenue, Acton (where the pros also used to train). Home games the next 2 Saturdays for anyone interested.
Can't say I follow their fortunes that closely, but from results so far this season, it looks like something of a 2 tier league with some absolute thumpings, but some more competitive games between those on a par with each other. This may well be to do with the major RFU rejig of the community game ahead of the current season where teams may take a season or 2 to find an appropriate level.