Shameless plug for an app I wrote to solve this problem:
https://simplebroadcast.app
Background:
I got tired of our Windows laptops deciding to update themselves right before "go" time, and I was unimpressed with the quality of the Teradek and the limited bandwidth of the stream feeding the Church's system.
So I wrote an app that could take a URL to an HLS playlist (.m3u8) and would remain persistent if the app crashed or Apple TV rebooted. When the app is re-opened, it immediately plays the stream it was last given. This is so much easier to give to another tech specialist or high councilman to take and plug into the projector at our remote buildings while I manage the broadcast from the stake center.
I also built a management platform that talks to an internal version of the app, so I get telemetry from the Apple TVs and know that they're having problems before the on-site guys can text me about them. From there I built my own transcoding and delivery solution as well because of limitations of the Church's system.
Eventually that grew to include a web-based player for our shut-ins so they could attend stake meetings. All of that combined then became the solution that we now use for all 17 wards in the two stakes in our city. (I've toyed with the idea of making it more widely available...)
Obviously, the Simple Broadcast Player app works best in a home-use situation if the broadcast URL doesn't change from week to week. Nevertheless, URL's can be emailed or texted, then pasted from an iPhone to the Apple TV via the Remote app (which is now a part of Control center in iOS). The Church's system does have an HLS (.m3u8) link that can be pulled and used with the app. It won't work for YouTube (unless you use the youtube-dl tool to extract the HLS URL from a YouTube feed).