For us, events and field team manages regardless if it is a client or net-new. Because field and events report into demand gen for us, that team writes all the emails: for clients, prospects, and for sales & CS to do their own invites. I don't touch/ own anything regarding client participation for events.
For smaller events, like we are hosting a client workshop as part of our enablement, I did manage that email. CS was on their own to write email invites, I sent them the email customer marketing sent.