I think it's regional. Not lived in Devon for more than 20 years (was in Tiverton for a while), but my recollection was a lot of fairly small, relatively self-contained communities and a heavy reliance on volunteer community groups to make things happen. I think it was Crediton that had a local, self-published newspaper that was indispensable if you were in town and almost incomprehensibly obscure if you lived more than 3 miles away. Cullompton might have done something similar. If the groups doing things like that have aged and not managed to renew themselves, they'll be gone now, of course.
Up here it's a bit different (or it was, pre-Covid). The university does a fair bit through its museums, some of the local churches are quite active with playgroups or fetes, the council has story time and craft sessions in its libraries and there are annual jazz, brass band and book festivals which usually have a fun day with free events aimed at families. Some of these might ask for a quid to contribute to snacks, but they were so cheap as to be effectively free.
The region also has some quite prominent museums - the Baltic in Gateshead has an excellent sensory room / craft area, plus lots of child-friendly exhibitions, the Glass Centre in Sunderland does glass-making demonstrations, often has colourful (if fragile!) exhibitions and a nice cafe with good views of the river, MIMA in Middlesbrough had its 'art trolley' on a Saturday afternoon, Discovery Museum in Newcastle has plenty of interactive exhibits and a water play area, Locomotion in Shildon is full of steam trains. All of those are free to visit, and they quite often had specific activities for children. You'll know better than me whether your bit of Devon has anything comparable - I can imagine Exeter might, but I wouldn't bet on finding this in Tivvy!
There's still community stuff going on - the village that has a scarecrow festival, the artists' cooperative creating transient artworks on the beaches - but to find it you need to be scouring the various village and community pages on FB. That can be a pain if you don't want a tonne of complaints about parking and questions about the local Hermes delivery driver amid the news of the bonfire night display or Santa's sleigh ride.