from your experience - when deploying a new version of my stack (lambdas only), Is there some downtime when neither the old nor new version of the lambda is available?

This should not be the case, aws makes sure there's no downtime

If you’re switching a stage from live mode to deploy there is a delay. Hence, never use a production stage in live mode unless absolutely needed.

I'm not seeing anything yet, we haven't gone live yet. I just assumed someone's done this before us 🙂 @thdxr so once we're live and I do

sst deploy

, there will be no downtime, just at some point a new code will handle requests instead of the old code, right?

Yep that's right, once your new function is ready AWS will start spinning up instances of it to handle new requests

sounds good, thanks!