Here's a free service that acts as a wrapper to Youtube or Vimeo live. It's geared toward churches but the "churchy" features can be turned off.
https://open.life.church
The nice thing is that it's truly only a wrapper, giving you the control to host where you want and decide for yourself if you want the streaming service to be free or paid.
It also has an Intercom-like chat function where mods see the backend and can share the load of
blocking people and doing 1 to 1 chat for direct questions. The chat can also have built in functions like pre-built links that are 1 click to
send to all viewers.
Looking at youtube though, don't assume all youtube videos and live events are the same.
You can have a Private stream where only those who have the link can connect and ads are a choice you can control. If you don't want to monetize the
channel, just uncheck the box. They do need to login to google in order to chat.
You can also make the stream unlisted but not private, so then you can embed the stream (just like you would a regular youtube video) onto any website, like the school website. In that case, you can utilize a chat that isn't part of youtube, like a free Intercom alternative - Drift.
The advantage to embedding the stream into your own website, even if its just a squarespace site, is you can control the chrome - what people see surrounding the video. You can have your own pertinant links, images, calendar for upcoming events
etc.
So if you really don't want to you youtube there's vimeo, but adding your other features, it's kind of
build as you go.