TLDR; No need to be concerned about using the church’s webcast system. I wouldn’t use it if I didn’t trust it. Licenses aren’t involved, and if they are, Bart needs to talk with me to fix that.

No licensing should be required to encode these streams.
Some information on the church webcast system. The virtual machines scheduled are WAY over provisioned per broadcast.
They do run in azure and of course azure has limits, but the church will not hit them. How do I know, I worked for Microsoft and know azure (as well as other cloud providers) quite well.
Each instance (or meeting for our case) combined with the muxing and HLS protocol for transporting the webcast can easily scale to over 2,000+ unique streams. Given our wards haven’t passed 100 concurrent sessions, and we have wards between 300 and 800 members, I’m confident you will be just fine.
There are more optimizations the church can do with the VMs and I know they are working on them.
BTW if you want to understand HLS (which Apple, YouTube, and Facebook also use for webcasts) here is the information on it.
https://developer.apple.com/streaming/