I have that Beelink and while I don't run Home Assistant on it (I run that from a VM on my NAS) , it does run a whole bunch of stuff, including Plex, and it's more than capable.
I think you have a couple of options here:
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Run HAOS on the bare metal and use Home Assistant addons to add the other functionality you want. Addons are HA managed Docker containers and there's lots of them out there, including Plex. What I don't know is whether you can access hardware acceleration this way, which you can do via regular Docker (see below).
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Install something like Unraid, Proxmox or whatever flavour of Linux you prefer - literally anything that supports full blown VMs and Docker at the same time. Install HAOS in a VM and use Docker for everything else. Passthrough /dev/dri to any Docker containers that use hardware acceleration (Plex) and you're golden.
It's a great little box. Enjoy!