They definitely do. One of my cats was depressed for months after another of my cats passed away.
Definitely, our 2nd cat really changed when the first passed on. Much more quiet and really affectionate to us specifically.
i've definitely observed this. my first two cats bonded super hard and after the first died the second was just miserable, for what felt like months.
When I lost my Chihuahua, my other dog and my roommates cats definitely acted a little off and we attributed it to them grieving. We also thought it could be them responding to our emotional state but we were never certain tbh
my cat let out a loud and long meow of anger and disappointment each time i brought my dogs home at the beginning and he seemed to only tolerate their presence; he didn't seem to notice when they died. he's an asshole but i love him.
Studies also find that cats will eat you face off if you die alone with them
