If you can run a light webpage with the tablet it should be enough. Owntone and homeassistant need to run somewhere else on your network like on a pi, or an old laptop.
Your app only heating controls may well also integrate with homeassistant, a hell of a lot of that kind of stuff does. Homeassistant also serves up a light web page as a control interface. There's phone & tablet apps too.
Worth a look, imho.
I'm currently running a raspberry pi with a 15" portable monitor (Here is one that is actually a touchscreen as well, mine aren't. https://www.amazon.com/ADPOP-Portable-15-6-External-Extender...)
For software I'm using magic-mirror, and then use that to link into my calendar, Home-assistant, weather etc. There are some input modules that can be added, so that might enable some touch-features.
I'm just renting right now, so I just have the Pi mounted in a case by the plug with some of those 3M picture frame strips and run the HDMI to the monitor (also mounted with picture frame strips) hidden in a track, If I owned, I'd bring the plug up behind the monitor, and flush the PI in wall and then wrap the monitor around a frame or something.
Just so it can be constantly on and display status while not requiring tethering.
I actually was building kind of monitoring screen; idea was to just leave it connected to ethernet and boot off network so it doesn't have any problems with SD durability or need any installation in case I wanted to have more than one.
There does appear to be a few Lenovo tablets which come with a permanent dock - maybe that's the solution?