Leave the media on the Synology.
Grab a NUC or similar small form factor for your Plex Server.
As @Xhaka mentions, Intel 8th gen or later with Quick Sync Graphics.
Kinks seem to be worked out for 11th Gen CPUs running Ubuntu 20.04. See this thread.
Not sure about 12th gen Alder Lake CPUs.
Linux. Windows has limited GPU support for tonemapping.
If you use Ubuntu, go with 20.04 LTS.
21.10 and Plex do not seem to play nice together. Also, 21.10 will not become a LTS (Long Term Support) release.
22.04 LTS will be available in April.