One screen, the whole party
You are not going to open a laptop to run a birthday. The guest list for your event lives on the page you built, and there is a view of it on your phone that updates as replies come in. You add names before you send, watch them tick off as people answer, and deal with the stragglers in the same place.
Every guest sits in a state you can read at a glance: invited but not answered, a clear yes, a no, or a yes with a plus-one attached. That last one matters, because it is where a partner or a child shows up in the count without a separate message to match.