I'm getting on very well with the Samsung Galaxy Tab A7, on which I run LineageOS; although a later model or something from the S-series may be more performant. I wrote this blog post about it.

I love LineageOS, but on this machine the bootloader cannot be re-locked and there will probably be someone about to reply to this comment explaining why LineageOS is insecure or whatever. Also, Samsung devices require that you have a Windows PC in order to flash ROMs, as you have to use Odin instead of fastboot.

Also, it's worth noting that, while /e/ is slightly superior from a privacy perspective, it is potentially less secure, as it sometimes takes months for the team to apply patches from upstream. Lineage, meanwhile, only takes a few days or weeks.

A cheaper option is the Galaxy Tab 5e, a mid-range tablet from 2019. It has a very nice 1600p Super AMOLED panel and it is supported by both LineageOS and iodéOS. I own one myself and it can do HEVC fine, but I'm not sure about those other codecs as I haven't tried them. I don't know what the availability is like where you're from, but here in Australia they are very easy to pick up secondhand in great condition for ~AU$200 which I think is a great price considering the quality of the display and their ongoing monthly updates.

GrapheneOS is the best for privacy imo. They only support Pixel Tablet (tangorpro) but I've ruled out google so ur going to have to use a different os which will be less secure.

Considering your use case u might be able to get a standalone display and put it in a custom 3d printed case with a raspberry pi and battery. I believe their are some similar projects online that are worth checking out.

U will struggle to find something cheap with an oled as its often used as a price differentiator for "premium" products.

I haven’t tried it myself but GrapheneOS supports the Pixel Tablet, so that might be an option! Not sure if the hardware meets your needs but it should be top notch regarding security and privacy!