you can solder T1-U-HL module ground and power to 3.3v/ground directly so TuyaMCU doesn't cut power to the module. This will at least let you navigate OpenBeken and upload your ready-made autoexec. Not sure if the display/TuyaMCU will work in that mode though. You'd have to connect power as normal to test properly.
There are lots of battery-powered TuyaMCU devices in the device list that link to many threads where the awkwardness around TuyaMCU in battery devices are discussed https://openbekeniot.github.io/webapp/devicesList.html