Nothing sends itself, which is the good news
One clarification first, because it is where expectation usually goes wrong: after a webinar ends, no follow-up leaves the building on its own. Before the session there are automatic reminder emails at 24 hours, 1 hour and 15 minutes โ the host can switch those off โ but the thanks-and-materials note is yours. You write it, you choose who gets it, you send it from the dashboard.
That sounds like extra work and it is actually the useful part. A message you wrote yourself, addressed to a specific group, is short and specific in a way an automated blast never manages. It can say what was actually discussed, hand over the thing people asked for, and name the next date without sounding like a template signed by a company.