I'm running latest Edge insider Beta on my Windows server 2019 Datacenter edition (AD/DC/IIS/ADCS/DNS/DHCP server roles)) (fully updated) and I have no problem installing extensions on it. (using Administrator account)
Beta channel has no controlled feature roll out so our Edge beta browsers are the same.
Are you trying to download your extensions from Google extension store or Microsoft extension store?
can you try ublock origins see if you get any errors and also which extension you were trying and failed to install? i'll try installing it on my setup