£2000 a term for 9-12 term time only sounds a lot! I think there’s better affordable options out there.
Many setting that are for 3 and above will give that for free using funded hours - you may be asked for a contribution towards snacks or asked to provide nappies of your child’s not potty trained.
Preschools and nurseries can’t ask directly for top ups to the funded hours. They CAN however apply the funded hours how they wish, so for example they can say you can only use funded hours between 11am and 2pm - which is a pain in the bum for most people and they therefore charge for the hours around it. Or no funded hours on Wednesday for example. They can do that.
However if you only need 9-12 from 3 years old you will most likely find it available completely funded, so I think ultimately you can save most of that £2k. Call around - many preschools are private businesses that would allow it so don’t dismiss private or state, just enquire.
I think the main differences between preschools can be quite stark. I’ve worked in one which was very much 100% child led all the time. We did circle time / stories / singing etc yes and laid out activities that were planned but it was completely up to the child for the whole session what they did.
The last preschool I was in did try to build the academic foundations more - we did phonics letters using the jolly phonics songs, and worked hard to get them recognising their name or at least the first letter. I personally didn’t start them writing and such because I don’t think that age bracket needs to be - there’s plenty of time for that, however I had colleagues who did start to push reading, writing and basic maths - some of it after parent pressure. The preschool attached to my school starts phonics from the word go (one academic year before reception) - I have mixed feelings about it - I think the most important thing from preschool is socialising, learning to play, building the physical and verbal skills through play, and building independent skills like getting themselves dressed and eating independently.
There’s so many lovely preschools out there OP, best of luck in your search. Don’t be afraid to ask questions!