I think it's helpful to remember that we want children to be able to concentrate for long periods of time in a regulated way, and the more they do it the better at it they become.
I'll disclose this by saying that I find playing woth children for lengthy periods of time hard, and anything I do is a skill I've learned.
I don't think it is sustainable to be continually interacting with children, and it doesn't allow them to process the information they have been given or for you to get the washing up done! I personally can't be doing with continual interaction, I find it intensely irritating, so it's not a huge stretch to imagine a child might feel that way too. They need time to be able to work out how to communicate their needs to you, to think about what sounds to make and experiment with ways to get attention. I read that a child needs around 60-70% of their interaction requests to be met in order for them to develop in a healthy way. Obviously for some traumatised children, this can be different depending on their early experiences, but it stuck out to me that you don't have to be "on" 100% of the time.
I would say that my 3 year old can focus on a task he enjoys with me in reasonably close proximity (he is on the patio and I am in the kitchen washing up) for about half an hour to 45 minutes on a good day. I check in with him by moving closer to him or commenting on his play sometimes, or just to delight in watching him build his own little world (I later comment on it so that he knows I'm thinking about him and that it is important to me), or if I want to build connection because we've been fractious I try to draw his attention to something I know he would like but doesn't interrupt his play- like "Oh my goodness, look at how bubbly this washing up water is! Do you want some for you cars?" And then leave him to it. I remind him I'm there, and that I'm thinking about him in a nice way even when he isn't interacting with me, and we move on with our respective business- me unloading the dishwasher and him making concoctions of sand and gravel for his snail potions. He surprises me by also noticing things I've done when I didn't think he was watching or would be interested, so we chat about that too.
On a bad day when he is dysregulated, I'm much more present, but that's not necessarily interacting. Funnily enough, my chores happen to be much closer to him, I'm more engaged in what he is saying or doing and I do verbal role play with him- i pretend to be a dog in distress that needs rescuing as im folding laundry, but i dont make it move or whatever. I try really hard not to be overbearing or interrupt him, but I'm purposefully present in a much more obvious way to coregulate.
We have 2 kids, so some of the play is with each other, but not all the time. Our day goes like this:
Wake up, one video then independent or joint play for about half an hour with their trunkis or upstairs toys whilst I get ready and tidy upstairs.
Downstairs, breakfast, nursery run for AS2, both on their balance bikes. Return home with AS3, I clean and reset (laundry, dishes from dinner and breakfast etc), AS3 plays independently for about 30-45 minutes with whatever floats his boat. Then we have an activity together (baking, painting, taking hisnbike to the park), followed by a tea break to talk about his snail hotels or car chases or whatever we fancy. Then he usually plays on his own for another 20 minutes or so before we eat.
Lunch with AS3, go to collect AS2 from nursery then drop AS3 off at his nursery. Walk back with AS2, he plays and faffs independently for about 20 minutes with his bike or dolls and buggy whilst I change laundry over and get his lunch ready. He eats and then it's naptime. He gets up about half an hour before we set off to pick us AS3 from nursery, so we do a quick activity together, or I quickly set him up with play prompts (oh look, I wonder if dolly wants a bath?), and he potters around and moves his toys from A to B as I do housework or emails. His favourite thing at the minute is to go into the garden, find sticks and put them in the locks of the patio door, so that's just great.... then bike and pick up AS3.
Then it's park time, AS3 isn't seen for dust as he is socialising with friends, AS2 kind of hangs round me looking for snacks like a small gannet, then wanders off once placated with a rice cake to halfheartedly go down the slide. We spend about 45 minutes in the park.
We walk home together, with them either racing each other so slowly a snail could kvertake them, or with them looking at various fascinating pavement treasures as I move between begging them to hurry up, playing lollipop lady as they saunter over the road and threatening to put a tow rope on their bike if they don't hurry up. I sometimes make up treasures that I've seen further on down the road to get them to move faster.
Then they play independently/jointly in the garden as I get dinner ready (now it is summer they have their paddling pool out and wash their bikes or water stones etc) for half an hour. They play together for some of it but not all, the sort of bounce off each other and parallel play. I make them tidy their toys away about 10 mins before dinner, then it is bath and bed.
Don't feel guilty for letting your child be for a bit. Some traumatised children can have had very little control over their environment, and so the ability to control their play and feel at ease in their environment is important for many, although they may have to be taught how to do it if they haven't already. We have a set of toys that are always available and then we rotate other ones in and out depending on how much energy I have to tidy up tiny bits of toy food or hear ceaseless sirens of emergency vehicles, but they choose the same things a lot of the time.
I try to be interested in what they are playing, and sometimes engage, but I let them lead and come to ask me questions or ask for stuff, and have set check ins to show my interest in their play and ask them how it developed. I also find it's easier to say yes to what they want when I haven't been giving them a million suggestions about what I think they should be doing for the previous hour. It allows me to watch them and pick up on trends in their play that I might have missed if i had been interacting.
My thought process is that I want them to concentrate, be curious about their environment, risk aware and independent. Therefore I need to provide an environment where that can happen.
I hope this was a bit helpful or reassuring. There really is no right or wrong way to do things, but it's about what's right for your family and you. Feeling frazzled because of the amount of interaction is tough, and can be really draining! Finding the right rhythm and routine has been key for us in having a calmer day in general.
Hope this is helpful!