I sympathise OP
My memories of 3 year olds is that they're not too bad to entertain but it is relentless and doesn't allow for much down time.
I've got a 12 and 14yo and they are an awkward age. We've also got additional needs in the mix to add barriers. I'd like to get out and do more stuff with them but they're just uninterested and we've done it to death over the years. Especially walks and parks. After 2020/21 they'd happily never see one again, and they have zero interest in our postage stamp garden. There are certain parks that DS1 despises and are a guarenteed meltdown. DS1 is also dyspraxic and loathes bikes. DS2 can't currently ride a bike or do much sporting activity due for medical reasons (so he's currently highly strung from not burning enough energy off)
They don't have friends in walking distance to casually hang out with. DS1 doesn't admit to having friends and has no desire to socialise out of school. DS2 mainly socialises over online gaming which is more flexible around his friends' contact time with family when they go away.
They're both very dyslexic so reading is a tedious, stressful chore not a pleasure. They're not generally crafty. DS1 does Warhammer but it's not a cheap hobby and needs pacing carefully. At a push he still Legos. DS2 can not draw at the moment because he's in a plaster cast.
They wind each other up chronically so shutting down tech and leaving them to entertain themselves just results in lengthy bouts of "brother baiting" which will result in upset. They haven't played nicely together in years. Things like board games always errupt into a row. DS1 has been known to stomp off before set up is complete. DS1 needs low sensory input and DS2 needs high sensory input so they just clash.
They just seem to be in a really awkward gap of being too old or too immature to fill their time constructively.
The thing that saves my sanity is a couple of structured sports continuing in the evenings, and both being old enough to leave for a few hours.
In the summer, we strategically go away in the middle of the holidays to break it into managable blocks. DH does pace leave through the year and uses a day or two here and there to break holidays up. I've also learned the hard way that DS1 in particular needs a buffer of a couple of low demand days to transition in and out of term/holiday mode, but he/ we do need to get out and about in the middle even if he hates it. His autism referral/ diagnosis followed a particularly gruelling summer holiday when he was 7 with several multi-hour meltdowns.
I love the DCs dearly. I've made huge sacrifices to meet their needs and time with them is not an idylic novelty. That doesn't stop it being hard to balance their desires to do very little other than numb their brains on computers with their need to use their bodies and change focus.
I'd love to go gambolling merrily around parks with them, play board games, cook, cycle rides or send them out to play with mates but that's not our reality and what actually happens is a few testy outings and lots of guilt about screen time. For perspective I try to remember that at the same age I was also into computers/ the SNES (pre-internet) although was more of a reader. DM certainly did not take me out umpteen times a week, and it was very much on her terms. I lived out of catchment so didn't go out casually socialising either.
So solidarity to all the loving mums out there who find meeting theirs and their children's needs over the holidays to be a slog. It doesn't mean we're doing it badly, and a lot of it is because we care!