I think that definition is missing something, yes. Modern(?) British twee is less "dainty" and more "manic and campy". Which is not to disparage Monty Python, who were good at it, but everyone descended from them can't really pull it off.

https://www.edwest.co.uk/p/the-unstoppable-rise-of-british-t...

(nb I'm not sure about the political analysis here but the citations are good.)