Thanks for your help.
My question is regarding the concept of bowing down/ crouching down to greet/pet an animal. There is clearly no religious intent whatsoever, it is simply a matter of reaching the pet to bow down/crouch down to pet/pick them up. I noticed that the question was asked regarding bowing down to reach a drawer and was wondering if the same answer would apply to the animal (as both have zero religious intention). Is it ok to bow/crouch down to pick up the animal?
As long as it is not being done with the intention of bowing, but for a practical reason, it is permitted.
Vein L’mo Mishchol 2 2-21, also see Kora Vovatz pg. 524 who brings numerous sources for this, such as Bais Yechezkel 1-chap. 7-19 in the name of R. Binyamin Zilber zt”l, and the name of R’ Eliyashiv, Avnei Yoshpe 2-7,