Our pet bird (sun conure) actively tries to lie and mislead when he's doing something naughty. Like he will go into the pantry to steal treats and quickly fly out pretending he wasn't in there when he hears you approaching.
This indicates he has some theory of mind. He has to understand there's a difference between what he knows and what we know, otherwise he wouldn't try to hide or obscure his actions.
And yes there is research showing/arguing that birds have theory of mind --> https://core.ac.uk/download/pdf/144146926.pdf