I've read your posts but not the whole thread.
It depends on the child but we built up from 10 yo. Things like 1-2h whilst I went shopping or to a gym class. My eldest is 3 years older than youngest. We had an occasional babysitter when we were going out out for some event like to some show or something in the evening. When they were 13 and 10, my eldest asked that we left them alone together the next time we went to the cinema/theatre (2h+ long) It's only a 15 min drive away and I kept looking at the phone, but it went well, were very responsible and I trust them. They don't mess around and either play computer games, watch a film or read in bed. So you'll know your children.
This year they are both in secondary and I had to figure out what to do for half term. I've had to leave them them for the full school day (9am-3pm) on the odd day and it was ok, but that's because they get up at 11am, watch TV, have lunch, play games and I'm back. When possible, I come back earlier to WFH the rest of the day, or me and my husband try to shuffle the schedules so one of us is at home. It's not always possible, though. Sometimes I've asked another mum if they could have my child just a few hours so it wouldn't be the full day, and it was also ok.
Saying that, I do use holiday clubs. However, it took me months to find something in my area, as they are not advertising themselves as such at this age. At least around here. One child does sports camps. The other one does coding or programming camps. These can be full days or half days. I've put them in these sessions because either I needed to work and it's some peace of mind, or because they wanted to go because it was fun for them to do, or because I wanted to have a day of peace and they like the activity. If you live near a city, there are probably some activities that you might have not found yet. I have now found 2 providers that do football camps, 1 for mixed sports, 2 for programming, 1 for theatre and performance, and the council does one with swimming and sports in the main leisure centre (spots go really quickly though). None of them advertises as holiday clubs or childcare because, as I understand, they are not "childcare" anymore in some administrative way or official status. They supervise the activity and you confirm that your child understands instructions and you are happy to leave them on the premises. There's some fine line around what is and is not childcare, I think, probably also requirements and red tapes. So they are "camps" and are focused on one activity.
Last summer I also sent my eldest a couple of nights to PGL with a group of friends because they wanted to experience it and they had good school results, so it was a bit of a reward. I think you can do 2 nights from about 10 yo. A bit expensive as something to fit in here and there, but if you can get a few parents, get a group discount, and do it in an unpopular week, it's nice for them as well.
I think the toddler years are hard. I love my kids to bits but when I look back at that period, I was a mess, always tired, always overwhelmed, with no time for myself, and had lost so much of my own identity. When they were both in school, I booked after school clubs a few times a week, and this also worked well. I started to manage better when they were 7-10 and soon afterwards I started to finally feel as my own person again. We don't have family around and we moved into this area without knowing anyone, so we don't have that network of support where you leave kids with each other. When I asked, it was because I had no other solution and it was always a very big favour. My kids liked museums when there were things for them to do, a cafe to eat, and we didn't spend more than a couple of hours. It always involved moving quickly from one room to the next and it was fun to some extent but more for them than for me. It was restrictive in the kind of things we could go an see as well. Nature, fossils, some paintings, perhaps some history or castles. It felt a bit like going on a school trip every time 😅 I wish I had been one of these mums here who could take them to all those fun places but it didn't work for me. It was mostly stressful, expensive, a pain with unreliable public transport, and I didn't have the energy even if they did.