Hi, teacher here. I'm overseas & we've been doing this since last March.
Non specific advice as obviously the OP needs adjustment for her dc's needs, but as a general thing...we are a) being zealous about safeguarding & b) covering our own arses. To be blunt.
Firstly, don't worry too much about the 'no bedroom' thing. It's safeguarding so that kids don't appear on a teacher's screen in their underwear/pyjamas or from their bed, or with their open wardrobe/personal items/dirty laundry on display - obviously you wouldn't want a non related adult having a window into their private lives. Fully dressed & in front of a reasonably neutral background is fine, so sit your dc in front of a relatively plain wall, & if it happens to be in their bedroom, whatever. We won't be popping round to check!
Secondly, devices - we have no real idea if your child is on a laptop, tablet, smartphone. Again it's a backside covering exercise so that we aren't encouraging 'OMG my child's teacher is chatting to her on her phone'. It's a not unreasonable hangover from NO PHONES school policies, because obviously you don't want your child & their teacher sharing SM etc - so for years teachers have been told categorically not to engage with students on phone apps. If a smartphone is what you have, fine - you are basically using it as an internet device. We don't know or care, but we can't officially tell you that because then we might get blamed for enabling/encouraging younger dc's phone use, & then your kid gets involved in inappropriate app use elsewhere... ('but dc's teachers say they need to have a phone for Zoom, so it's their fault he's been bullied over Snapchat/she's been up all night TikToking with randoms').
Thirdly, the tutor group sessions might actually be really good! Dd2's form tutor has been amazing throughout. Ds & dd1's, less so, but it's been a quick 'oh hi good morning' before they go about their day.
Fourthly, an adult presence is AGAIN to cover safeguarding. To be blunt, if you try to sue us because your dc got sent a rude picture by a classmate during tutor time & you decide that's our fault, our response/defence is '...but the policy says you should be supervising?' It doesn't mean you need to sit alongside your dc throughout, just ideally be in earshot. Equally the 'nobody else in the room' rule is mostly so we don't have your dp/older dc hovering in the background in their pants (Fit Dads in Swimmers was definitely a thing last Spring here - might cheer up some of the teachers; inappropriate to expose other people's teenage dc to it...)
Ultimately, teachers have been trained for years to be super cautious about contacting your dc online. We are careful. We also can't risk any loopholes which make it our fault if it goes wrong because your dc isn't fully supervised - hence the possibly overly stringent 'you need to do X,Y & Z' directives - schools have tried to imagine every dodgy scenario that could occur.
Anyway - OP - just let your dc's school know why this set up doesn't work for you. It'll be fine, honestly...