The Pi won't cast from your phone, so Im not sure how you will make things better if using your phone is must-have. I also use cast as my main way to watch stuff, and i've experienced my cast devices not being found from different phones and same apps. E.g. the pixel phones find the cast devices (chromecast, and a hi-fi system that has cast abilities), but a Realme no-name chinese android phone won't. Or that my chrome browser can't find the cast devices either, no matter which OS is used under (I have to cast the whole tab).

And even if you install emby or jellyfin on your raspberry pi, the app might not see the casting device. It'd work better if you just don't cast, and instead just direct emby/jellyfin's phone app to play the media on the raspberry pi connected to a tv.

Also, be aware, that 1 GB of ram is not enough to use emby/jellyfin. I have a raspberry pi 3b+ with 1 gb of ram and it swaps like crazy when i use these media servers (music only). Minimum is 2 gb, best if you can get it with 4 or 8 gb. If video is needed, you will need a Pi5 for best results.