I have searched and searched for ways to get google messages text messages to my Active 2, and from what I can tell other people have the same issue. There seems to be no solution. I, like a lot of people, like to use google messages while on a computer, and it is extremely inconvenient to switch back and forth between Samsung messages and Google messages. In fact more recently, I can't even get Samsung messages to alert on my watch despite multiple attempts to change notification settings etc. I hope Samsung changes this because I am at the point where I am ready to never buy a Samsung watch again. If they can't fix this problem and allow us to download google messages to our watch or get notifications, they should at least come up with a web based Samsung messages feature so that we can send messages through a website like Google messages. I'm so over it. If anyone has found a solution (even if it involves downloading multiple apps), I am open to that, and please direct me.
I have a Note 20 Ultra 5G which I use with my Gear S3 and Galaxy Watch 3. I use Google messages and have no problems getting alerts and messages on my watches. I did nothing special, it simply works.
I would recommend that you try clearing the device cache on your phone and reset your Active 2.