While you can pair up to 3 watches to a single iPhone, you can't share one Wearable plan according to reports. So if you want 3 Cellular models, you pay $10 for each.
On your specific plan, that's a hard one since it makes no mention of Unlimited Data. However, you might try going to a AT&T Corporate store and giving it a try.
Just keep saying I trying to add a $10 Wearable plan to my account. If the first response is that you need a Mobile Share plan, suggest the rep try adding a new line group and select an Individual plan instead of a Mobile group. Once the Individual line is selected the rep should be able to quickly find the stand-alone $10 Wearable plan. Make sure you have to watch's box for the IMEI and EID numbers that the rep needs to add to this new line. It would be even easier if the rep could activate the line.
Yes you can try phone reps but they have had some training on "not" to active a watch on these old Grandfathered plans. No technical reason, just a policy / business decision.
Note: Your watch has an Embedded SIM(eSIM) so the rep can't swap SIM and you don't have ICCID number to give to them to add to this new line. The eSIM is provisioned with a ICCID during the Set up Cellular steps done on your iPhone using the Watch app as it interacts with the AT&T system.
Dave