@Anon2136 We were in a similar boat last year, although ours were a little older - we already missed the start of Year 3, and had another in Year 5. Local state school started out great, it was a small community school, Outstanding ofsted, well-regarded in the local area.
Even before the pandemic, I thought the school were not really pushing my children enough, and during and after the pandemic, there was a real decline in the standard of education being provided. Even when they were back in class. Similar to what you say, teachers just didn't seem engaged in their development, no work being marked, etc.
I'm not blaming the teachers, I know how tough it's been. But at the end of the day, our children are put through the education system only once. They only get one shot at learning through each stage - so I looked around for prep school places, and we were very lucky to find a place for one child, followed by the other.
The difference in the attitude to learning is vast. There is such a positive atmosphere in the prep school, and my children are so much more engaged with their learning. They find learning fun now, whereas before they would constantly tell me about how disruptive the class was. They would have been happy to stay in the state school, but they didn't know any different.
It was a difficult decision to make, not just financially, but also concerns about if they didn't settle in the new school, especially for the older one. However I think once you start getting doubts in your mind about the current school, it's really difficult to ignore those niggling issues.
Whatever you decide, best of luck. However if you do decide to move, try for Year 3 - they work around a year ahead of state schools, as some prep schools do help prepare for independent secondary school entry (if they only go up to Year 6). There has been less focus on grammar school entry (different type of exam) as many parents stick with the private route. Also I was surprised to learn that many of the parents still pay for additional tuition - I don't think that's necessary, but each to their own.