Depending on the complexity of the game and how long the story already is, I would either quickly catch up again (like just holding ctrl) or stop playing for a while (either wait till it is finished or until it has been long enough that I won't get annoyed replaying).
I already played Innocent Witches 4 times until stopping and waiting for them to rework everything I already knew by heart. Now I've started my 5th run because it has been sooo damn long I wanted to try it again.
Depends on how much I like the game, and so long as I can fast forward through the parts I have already played I don't have a major problem playing again from the start. However, if it is a game I'm not too interested in then it just becomes annoying and I drop it.
It is bound to happen as in you are playing a game in developmental stage so I don't mind it. By the way I don't include those grindy sandbox so not a waste of time if I replay the game as I enjoy the story
When that happen or when for some reason I have lost the save, I generally stop playing the game until a couple of updates later, unless the game is not that big, if they are small I just go ahead and play again as long as it's not been that long ago since I have last played
Nah, I play from the beginning if I have to. Sometimes I even do it just because I feel like it. Losing my saves in a VN doesn't matter at all to me. One of my favourites (though, to be fair, it's less of a VN and more of a legitimate management game at this point) is the Lab Rats 2: Reformulate mod. Losing my saves doesn't matter at all; I regularly restart that game whenever an update comes out due to the number of early game changes that arrive with each new version.
And I like seeing scenes in context again. A new update gives me an excuse to do that, and also to refresh my memory of what the hell actually happened in the (admittedly often paper-thin) story prior to the new content. I don't think I've ever actually opened a scene gallery in a game, even when it's prominently offered to me, just because I don't like watching those moments in isolation. If I'm not seeing the lead-up, the payoff doesn't do it for me.
In short, updates messing up old saves means nothing to me. I'll play the game from the beginning again, because I was going to do it anyway.
One of my biggest peeves is when a game announces, restart the game and doesn't specify from which version. Its just stickied in the thread for all eternity, so how am I to know if its from 0.3 or from 0.8...
Really depends on the game and how far into the updates I was in. Like if last I played was only 2-3 updates then I can start over. If I'm like 8 updates in. I'll probably not. Unless I'm really deep into the plot and characters. I'll just fast forward skip everything and do the same choices.
But also also depends if it's a straight forward VN vs a VN with a map, unlockables and grinding. Then I'll probably drop it
I'm more likely to look for a way to cheat the damn thing so that I can return to a relatively similar point, especially on a grindy game. What usually happens is that once I start, I never really play it properly again, just force it to show me the new content after each following release.