Well I might slap you if you rubbed my bellyI don't know. My understanding was that it was a surprise research finding specifically in cats.
It is a very dramatic effect - she goes from a hissing, spitting monster to 'whatever'! It takes a couple of hours to wear off at home and she is a little wobbly on her feet - not too bad - basically she sleeps it off. But it is amusing to see how chill she is. She even purrs when you pet her tummy (normally she might bite if you do that uninvited).
Anyway, it is a game changer. Taking her to the vet was so stressful for her and therefore for me. She looked like she would explode and take the vet techs down with her.

I would say both Pregabalin and GBP will become an anti anxiety med in the future. It’s already being used off label for that.
Anyways I found this for pain control in birds
https://www.dvm360.com/view/updates-avian-analgesia-proceedings
Seems there is still a ton we don’t know about bird physiology.