I don’t know if you can build for Tizen 6 (which the TVs are updated too) and run the app in the older emulator.
To Run the emulators be sure you have the older Java 8 in both the Windows and Mac Mojave they won’t run with the newer Java. I’m not sure if you need the 32 bit Java in Windows or 64 bit version I don’t remember if TS 3.1.x was 64 bit but I think it was. (all Mac versions are).
Good luck on Big Sur on the Mac it is a real pain. I think anyone that gets it to work runs Windows on the Mac Big Sur.
This isn’t my area so take what I say with a skeptic approach it may be off and my memory surely is. The notes for the old Tizen Smart TV was on a previous forum.
Ron
Samsung Developer Relations