Personally I think 3 is too young to call on PDA, although I agree that the framing of the behaviour as stress-related rather than wilful choice is vv helpful. It is unlikely you'll get very far with time out, for example. Some online representations of low demand are unhelpful, IME. I don't think it's usually helpful to bend absolutely everything around the child's feelings, and as you point out, sometimes accommodating anxiety behaviours can make the anxiety worse. However, it can help a lot particularly temporarily to reduce pressure by dropping unrealistic demands or expectations.
I do wish the word accommodation wasn't used both in the context of accommodating anxiety behaviours/compulsions and accommodating needs in the case of things like autism. It's confusing and it sets up this weird thing where accommodation is seen as a negative in certain contexts and a positive in others.
I find quite a useful framing rather than accommodation is around autonomy and responsibility. So I would avoid accommodating demands which threaten somebody else's autonomy - ie, I have sat down and child says no, you can't sit there, you need to sit here - I would say no, it's my choice where I sit, or I might say ask nicely and then I'd be more likely to follow the request. I know this seems like a very small thing to let them win on, it's just to me about being clear where their autonomy ends (dictating the behaviour of another person). We are generally clear when it's a situation that you can ask/request the thing from the other person, and when it's not (and when it is an ask/request, that the other person is also allowed to say no).
But if child says they want to wear shorts in the middle of winter I would probably try to accommodate that in pursuit of supporting their autonomy. Perhaps it means we don't go out - fine if we don't need to go out that day. If we do need/someone wants to go out and toddler needs to come with, then we'd look for some kind of win-win problem solve where toddler maintains control over their clothing, but I ensure they are not at risk of frostbite (responsibility) - which might look like different clothing options, or bringing a back up option, or using a blanket in the buggy or staying in the car as long as possible.
Then there are situations like child lets me know (perhaps in a not ideal way) that they are struggling with the sensory input of me singing/humming. At 3 I'd probably take it as info and try to stop humming. For an older child I might look at it more from the other people's autonomy thing where they can choose whether to go elsewhere, use ear protection, etc, or request the person stop more nicely.
Do not accept home education if you don't want to do it. Keep pushing for education which meets his needs. The LA has a duty to provide it, though their budgets are empty so they will be constantly triaging which DC have the highest potential consequences if they don't get this, which means the majority of DC miss out. This is unsustainable, so do use every resource you can for this. Contact local MP, look at appeals charities, support groups, anything.
Mona Delahooke and Conscious Discipline will probably be your most helpful resources at this stage. Conscious Discipline is a pain to navigate (their website) because they are aimed mostly at schools but they do have content or advice which is transferable to parents, and it's very well presented.
IME, at 3 regulation is close to 100% co-regulation, which means that he needs time and space to build close, trusting relationships with new adults and he may need proximity to a trusted, safe adult close to 100% of the time. I think this is why it tends to work well in 1:1 situations like therapy but can be trickier in group situations.
And at this age your co-regulation is almost 100% physical. If you think about the body language you'd use to approach a frightened child, or a wild animal, it's this. It's understanding where his behaviour is coming from so that it is less likely to trigger your own threat response and put you into fight or flight, and then consciously modifying your body language so that it communicates safety - being small, moving slowly, voice should be low in pitch, volume and speed, avoid demands, avoid threats. Physical touch may help or not, try to see. Eye contact may help or not, try to see. Don't expect actual words to go in, so don't talk very much or just say validating/soothing phrases.
Keep modelling things like deep breathing rather than asking them to do it etc.
Once calmer, they can often problem solve better anyway or they have moved on from whatever the issue was. Try to pre-empt hunger, toilet need, tiredness, physical exercise need (all easier said than done!)