For your points 2 and 3 specifically: if you go the Icecast route (AzuraCast also uses Icecast under the hood), Icecast can require a username and password per mount point, so the stream URL alone is useless to anyone who stumbles on it, and you can give the mount a bland name. Put it behind HTTPS on your reverse proxy so the password isn’t sent in clear text.

For point 4 (genres at certain times), AzuraCast’s playlist scheduling handles that from the web UI. If you build it yourself instead, Liquidsoap can switch playlists by time of day, but it’s a scripting language with a learning curve.

If what you really want is your own library rather than one stream everyone hears at the same time, the Navidrome suggestion is simpler: separate logins and plenty of Subsonic apps on Android.

If you’d rather keep Vikunja as the backend and web UI, it has a CalDAV endpoint, so you can point DAVx5 at it and use Tasks.org or jtx Board on Android for the reminders themselves. That gets you native Android notifications without email, and you keep the web interface for planning. Vikunja’s CalDAV side is less mature than its web UI, though, so test whether due dates and reminders come across the way you expect before moving everything over.

For notifications that aren’t tied to a task app (say, “remind me when X happens” from a script or Home Assistant), ntfy is the simplest self-hosted push to Android, as mentioned above.

If you end up running it headless (game streaming host, Jellyfin/Immich worker, whatever), two small things save a lot of hassle:

• Get an HDMI dummy plug (a “display emulator”, a few euros). With no internal panel detected and nothing on HDMI, the GPU often has no proper display to render to, and Sunshine/Steam streaming in particular wants a “real” display to capture at the resolution you pick.
• Check the BIOS for a “power on after AC loss” / “auto power on” option. Plenty of laptops don’t have it, but if yours does, it comes back on its own after an outage like a proper server. Otherwise Wake-on-LAN from one of your mini PCs is the fallback.

And since storage is your bottleneck right now, open it up and see if there’s a second M.2 slot. Some of these chassis have one, and then it could hold some data while also taking the Immich/Paperless ML jobs on the 3050Ti.