My T and I always just had sessions over the phone without video, but I can totally see how it would be distracting to have the background/location change suddenly.

I think it's fairly normal for a lot of people in therapy to wonder about things like 'what does my Ts house look like, what does he have on the walls' and so on. My T has a picutre of himself on his website, which I'm pretty sure was taken at his home. I have analyzed its background to bits, even though there's almost nothing there. I assume I'd do the same if I actually saw him on video there.

To me, consistency is quite important. There's certain things I've come to appreciate about my T even though early on I found them rather weird. For example he always dresses the same way with very, very little variation. The most adventerous I've seen him is wearing a red shirt instead of a blue one. And the first two times he did this (after about a year of seeing him), it was actually very distracting. And that's something that doesn't even really tell me anything about him, unless I'd have assumed that he has never, ever worn anything but blue before...
I'd not necessarily want to know when he's in a different location. Similarly to how I don't need to know before coming to the session that he's wearing a red shirt. I got used to my T wearing a red shirt, I'd get used to a few different walls, lightning situations and chairs over video. But I'd need there to still be some sort of consistency. Like it's not a red shirt, then a yellow one, then black, then completely different style of clothing and so on and it also shouldn't be a different room every time. It might take some getting used to, but after a few times in each location it'd probably be fine for me.

I don't think I'd necessarily be bothered to just notice the change in what the stuff around T looked like (like if there's a different plant in the picture, or different painting), but I'd be bothered if I'd had to worry about seeing personal stuff that I'd normally not see. My T has a few paintings and plants in his office, I didn't care much about them when I first started seeing them and still don't. I think it'd be the same over video. But I'd have cared and probably not started to see my T if there had been photos of people for example. And I'd not want to have to worry about whether personal things like that might be visible every time I start the call with my T, having to scan the room and so on... so if the location or background sometimes changed, I'd probably talk about it with my T so he knows that I'm anxious about that, so he could always pick a neutral wall in the room before starting the room or something like that.