I wanted to come on here from the perspective of a parent who really did not enjoy playing with my DS when he was very little and who was the parent of a child who had a lot of behaviuoral difficulties. Whilst this isn't exactly the problem you have op, I just wanted to extol the virtues of playing with your child
DS was often very clingy and demanding of attention - almost constantly at one point which I really struggled with but this book really helped me Playful Parenting
It is a bit old now but it gave me so many good ideas about how to deal with DS when he wanted to play the sorts of games I didn't (ie fake shotoing and fghting with sticks) in a way that worked and that didn't involve telling offf or being critical.
One important idea it passed on to me is that if we can give our children some regular time to play with us in a way that is completely led by them, that this will really help their behaviour and our relationships. This really did work with DS.
A couple of times a week, I would set a timer of 30mins and tell DS that this was play time . He could decide what we played and I was completely led by him. The only rules were no hurrting. We sometimes wrestled, we sometimes played with his action characters, sometimes we built forts and told stories. It was all led by DS and I followed. I sometimes found it hard to completelly stay present , especially when we were playing with his action heros (yawn! ) but the 30 min timer helped with that. DS was not a child who wanted to do quiet activiees - like ever !, so I had to have the energy for his games which were 90% of the time of the physical variety. Quite honestly, I'd have loved him to be happy drawing and doing jigsaws.
When the beeper went off, DS was always much less clingy and difficult to please for quite a while afterwards and we both felt a lot closer to each other. Over time he would suggest the 30 min play and this was usually his way of saying he wanted to reconnect for whatever reason. We couldn't always so it immediately when he asked but we would agree a suitable time and I always kept that agreement without fail.
I am firmly of the opinion that this practice helped save my relationship with DS (who has ASD and ADHD and whose behaviour was often difficult to manage when he was younger) and I think it helped him moderate his behaviour. During our wrestling bouts he sometimes went too far, but my response was always 'no hurting' in a calm voice, if you do that again we will stop the timer early. He never did it a second time and over time even the occasional hurts stopped as he learnt to control his natural enthusiasm while we wrestled
This is just by way of saying that putting aside time to play with your child is never a waste of time (even though it can feel like that, and in fact I really struggled with it). And by that I mean letting the child lead and playing what they want to play, not what you prefer to do
Whilst it is probably not as necessary with NT children, for DS it saved our relationship which had got very strained by his anxiety driven behaviour and which I was struggling to manage calmly at the time
Just my experience op