Hard find to have a "cheap" Android tablet that gets longer term Android support or has a development community supporting it with custom Android versions (e.g. LineageOS). Maybe start with the LineageOS supported devices. Note: some of these are on older Android veresions but they are at least still supported with active builds and the current month's security patch. Pixel Tablet would be a good fit but it's far from cheap.
Most other cheap tablets you look at are going to have a locked bootloader making rooting/replacing the operating system impossible, and not that long of a support cycle from the manufacturer. You can give up the dream of finding something like that and just get whatever cheap tablet, likely the Home Assistant app will work indefinitely on it until you go to replace the tablet.
Yeah, would be nice if Nvidia released another Shield tablet; I think it was supported longer than most Google Nexus tabs even. And I actually still use mine on a daily basis as a second screen companion (keep Discord feed up in mulitplayer, Youtube walkthroughs in games, etc.) on a stand next to my PC. But sometimes it chugs hard, esp. after a reboot for a while, so would like to find a decent ~7" tab to replace it at some point.
If you want cheap android tablet, maybe look at the low end Amazon Fires... Probably zero upgradability, but fairly wide install base, low cost, and you can probably buy a new low cost model when yours poops out.
We've had our S8+ samsung for a year or so I think and I like it, it's great for storm chasing with the 5g and the screen is fantastic for radar and music at the same time, and the sd card slot for hordes of topo and street maps and music.