Why don't you use the original package name for your mod? What is the benefit (or workaround) of having a modified package name for the mod when all people could uninstall the original SHM app on their watch so the mod would install without an issue on their devices?
You can't remove the original package from the watch4, you are only removing it for current active user, SHM can be restored by doing the adb command "adb install-existing <SHM package name>", the command will go to system files and restore SHM, and no, you can't do "adb install <SHM package name>", it will throw you a buildtype error (-3001, INSTALL_FAILED_REJECTED_BY_BUILDTYPE) because you are trying to install an existing package with different build even though, as I said, you did adb uninstall for active user, not system...
Think of the uninstall process on the watch4 as equivalent to uninstall updates and disable app on the phone, you didn't get rid of the original app on your phone, most of non-root users disable apps on phone as a way of debloating...
Most android apps (including the WearOS ones) have a signature verification so when they communicate, signature verification must pass, if the signature fails, the communication ends...
That's why Tizen SHM MOD (Original Package Name) and the Watch4 keep throwing signature failure and refuse connection, the only way to remove the original package from the watch is rooting the watch, voids the warranty (that is not what we want), the other solution is a different package name, cons? well pretty much everything is patched to work, aside the pros of having two SHM mods, one for Tizen and the other for WearOS that can work in parallel...