Free and Open Source Software
If it's free and open source and it's also software, it can be discussed here. Subcommunity of Technology.
This community's icon was made by Aaron Schneider, under the CC-BY-NC-SA 4.0 license.
This is usually a function that full blown media servers offer.
Jellyfin is the one that jumps to mind with this functionality, however I haven't really this functionality out as of yet.
Jellyfin's watch-together-feature (can't remember the name) worked very well on my local network when we needed it (remember Covid? +__+), so I guess it could also be an option if you do it with Wireguard or something similar.
Browser-based, but works on mobile just fine: https://www.watchparty.me
The amount of viewers you can stream to depends on your upload speed and video bitrate. There's a premium version that allows relaying video files via their servers.
It's also open source so you can host it yourself should you want to.
This is just what I needed! My group has been using Discord for the longest time but it very frequently turns into a 144p stream