I'd rather play almost any game in first-person rather than third-person. A game in which I'm a cat might be one of the few exceptions. If you feel differently, and you'd really like to get inside the head of the feline protagonist in Stray, then there's now a first-person mod to help you.
The Stray first-person mod lets you play almost the entire game through the cat's eyes, which means the camera is much lower to the ground than you're used to. The immediate sensation I had upon watching the video below wasn't "hey, I'm a cat" but "hey, noclip is turned on":
You can download the Stray first-person mod created by Jessica Natália from Nexus Mods. There's an included readme file which explains how to set it up. You can also find more details over on MixMods.
The mod does have some limitations. Sometimes, when running or jumping, you'll see a brief flash of the procatonist in third-person. There are also some moments in the mod which will necessarily remain in third-person so you can "see some destinations, or chases". If you do encounter a point where progress is "impossible or too difficult", the developer's notes suggest removing the mod file, passing said obstacle in third-person, then returning the mod afterwards.
Given that Stray has only been out for a week, it's impressive that there's a first-person mod at all. It's not all Stray modders are doing, either - they're also replacing the cat with Garfield models, dogs, or CJ from GTA: San Andreas.