I was told that the Tizen 2.3.1 will run on Tizen 4 but not optimal Which is why you get the warning.
I would suggest you create more than one binary one for the Gear S2 like you are and then build one with Tizen 4 for newer Galaxy Watches.
I believe uploading to the store is the same for Tizen Studio as it is for GWS. Here is how to do it for GWS
Build two .tpk files one for Galaxy Watch (Tizen 4.0) the other for old Gear models (Tizen 3.0 or less)
You need to build twice, for each build you should set different Target API version and enter different version number.
In your build settings
Package name should be the SAME
Version should be different
Target API version should be different
In File Manager you will see that both a xxx_TW3.tpk and xxx_TW4.tpk files are generated.
Upload both files at the same time.
Upload First binary
Select add more binary
Upload the second Binary
The result is that two binaries have been updated. TW4 will be downloaded by Galaxy Watch (Tizen 4.0 device) and TW3 will be downloaded by Gear S2 and S3 That haven’t been updated. A notice will appear don’t worry this is standard.
Samsung Developer Program