This answer doesn't say why we got these login prompts.

Does anyone here know why many of us had to log back in to our google accounts?

Same with this answer. Doesn't say why (although this question didn't ask why).

Are there any security disadvantages of automatically increasing security when I get new sign-ins? I'm currently using pbkdf2 with a target time of ~1 second. I was thinking I'd time it every time, and if the time started to drop below ~.9 seconds, I'd increment the iterations and update the stored hash.

@WilliamMariager One second is quite a lot. That makes preventing DoS attacks difficult. I believe 10-100ms is a more common choice.

But in principle I think automatic increases are fine.