Good question actually. Docs say
Any variable accessible by twig
So page should also be available, but now I’m thinking if this might be related to the issue, where form might not have a page 
@anon76427325, any ideas maybe?
I wonder what actually page should be in this context - if it’s a front-end form, then I’d expect page to be where form is outputted, or in module case, maybe a module page itself