Sorry, initially posted this in the wrong category…
Hello and welcome! I think you’ll find the people in this forum to be quite friendly and inviting.
Yes - bees are winter prepping and I wouldn’t recommend you add the flow super or plan to take any honey this year, especially considering that there isn’t excess honey in the brood boxes.
I wouldn’t recommend splitting at this time of the year. The bees are unlikely to swarm in the late summer/fall especially if they have a young queen and aren’t out of space in their current location.
Making sure the tray is clean and the bees don’t have excess space to defend (and high proportion of workers, if you ask @JeffH) should usually take care of SHB. Having the hive in a sunny location helps too, but make sure they don’t get too hot in your location so some afternoon dappled shade would be good.
You might search the connect with locals category - and maybe be more specific about your location… Texas is quite vast and varied.