There are certainly other problems with the system including Ford's own updates that break things. It's good that you don't appear to have BT issues now but it's a potential whack-a-mole problem inherent in the system design.
Perhaps you could put a clamp meter on the 12V battery to see if there is noticeable battery current difference between working and not working conditions.
I have tried that already with my 2022 Lightning. In the past thinking the battery was the issue a running car was parked in front of my Lightning. Jumper cables were strung between the running car and the lightning increasing the battery voltage in the lightning. If I remember correctly my Lightnings battery voltage went as low as 11.8v with the truck parked for a period of time. With the cables attached I think the voltage went up to above 14v-15v. (it has been awhile since I did the test so I'm not exactly sure of the exact voltage once connected with the jumper cables). Increasing the voltage still did not activate the truck to return DC to the house. So in conclusion, I feel it isn't a voltage issue. It is more system or systems are in some type of sleep mode. I think, pressing the disconnect button, unplugging the charge cord, waiting until the white light goes out on the truck at the charge port, then reinserting the charge cable is one way to wake the system up that powers the house.
Agreed, owners of the HIS systems have spent good money on a system that is advertised by Ford to power your home. Seems us HIS owners are being "left in the dark" with absolutely no support besides a promise, "a fix is coming" Do you think if you bought a TV that would not change channels and you called customer support and were told, "you will just have to watch the single channel but a fix is coming" would be acceptable. I think not. Fix this thing or give me my money back including the cost to rewire the service panels. I'm tired of "a fix is coming"
