Also a friend in Sheffield runs https://www.forestschools.com/ - they have a few of their own schools in the area, and then run training sessions for people that want to run their own.
Most of his training is in the UK, but it is a full time job for him and his team, so I can only assume either there are loads of forest schools opening up, or people just like doing the training and then apply the learnings to 'normal' school processes.
My kids school is a standard state school, but they all do one day a week 'forest school' from the woods that form part of the school grounds. I doubt they are on the 'forest schools' list.
450-500 in Denmark here's a good research study including impact on ongoing educational attainments: https://nexs.ku.dk/forskning/idraet-individ-samfund/krop-lae...
About 1000 in the US: https://naturallykatey.wordpress.com/2021/01/08/list-of-fore...
Plenty in the UK, Spain and France too.
There are more projects for early years education than later, and they very typically don't have websites or much digital presence.