Hmm, there aren’t limits in place for this, as school communications are an essential feature and not ideal to limit, and there are also messages sent from other areas of Gibbon to consider.
One thing to look at may be to use the Gmail SMTP relay, which is an SMTP server that can send a lot more messages (up to around 2000 per day generally without issue). There are also paid SMTP services, see the post here for more info: Important update for Gmail SMTP Relay through Google - #2 by sandra