I've just had some really frustrating support sessions with Samsung support.
I'm currently roaming with my s9 and galaxy watch, no matter what I do I cannot get my watch to display the local time
1 agent suggested unpairing the phone setting the time and timezone manually and then repairing. That didn't work.
Even when I set the time manually on my phone my watch still shows the incorrect time.
The only way to successfully do it is to disconnect the watch and set the time manually on the watch but then I don't get notifications etc..
1 agent said that as the watch was sold in the UK it will only ever show UK time. I think this is not true and they just didn't know the answer. If it is true then this is a massive oversight from Samsung and makes the watch essentially useless when travelling.
You have to ensure that on your phone in Date and Time settings you have Automatic Date and Time ticked. I had the same problem as you and it turned out it was my phone using manual time.