If you can dedicate a Raspberry Pi to this, you might want to consider Volumio. Visit https://volumio.com/en/get-started for more information.

You could implement the schedule play music with just a cron job triggering playback via the API

I dont think this exists. Maybe you can use an existing server and player and automate it with home assistant

Picoreplayer can do that, if you run the lms server and client on the same box. It'll be slow with large collections on a pi but it'll work. You can play a track or playlist as a scheduled alarm in the player settings. The only real trick is scheduled pause times, which could be handled using the PowerSave plugin or from the router https://forums.slimdevices.com/forum/user-forums/logitech-media-server/107222-pause-specific-squeezebox-at-scheduled-times#post1375971

https://moodeaudio.org/

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To upload music you can check this list

Not sure if moodeaudio supports timed playback...