I had three other thoughts I'd like to share:
I have Captcha login on my GT-AXE16000, I just checked the specifications to make sure I have it. I do believe I've seen it in the past, but I don't know what I clicked or option I selected but I haven't seen it in a very very long time, mabye just that once. Being as it is I'm not sure if it's an important consideration.
I have a 6E router (as noted) and I do believe there is backwards compatibility with IoTs so I am not sure staying with WiFi 6 is a necessity, it may be a matter of more money, which I definitely understand as a concern. (I have a friend who's happy with his $30 router, and I'm happy for him)...
From that I can say that 6 GHz backhaul does work, through at least one floor, and maybe 10 - 15 ft of horizontal distance. (They are positioned at roughly the same height I would say). In fact my AXE11000 and AXE16000 were preferentially on 6 GHz vs 2.5 Gbps ethernet backhaul for maybe 1 - 2 weeks. (I have it set to automatically choose). If you can find a store that would let you try a 6E router and return without penalty if it doesn't work out then I would definitely consider it. 6 GHz is not as crowded as 5 GHz and may work out better as a backhaul.
BIOS- Yes I took a look at both and the XT12 has 2 new beta versions made available this year. The GT6 has release versions available this year, (the only ones as it's new). If I had to choose based on this the GT6 would be better as it has release level BIOS from this year. I did take a peek at the more expensive ET12 and the latest dated 2023/04/13 is a release level firmware. (Obviously they are more focused on supporting the ET12).
