As @l_l said, every single script using API v1 would have to individually be updated. Someone could of course make their own copy of a given script and convert it to API v2 themselves, but even then they can’t update someone else’s script on Tampermonkey. They’d have to save a new copy to Tampermonkey, which others would have to manually switch over too.
So to this point, no this doesn’t have to happen, and likely won’t for every script. It’s a near guarantee that some scripts will be abandoned when API v1 is discontinued. If a script is popular enough and the creator doesn’t update it, someone else may choose to make a new version of it that works with API v2.