GMs - how do you handle mundane animals, like dogs and cats? Say someone takes the Animal Companion talent and wants a cat... how would you handle that? Would you give said cat a profile? If so, how would you build it? I'm really struggling, so thoughts and comments and assistance is greatly appreciated.

Typically, things like that don't need full stats. If they just want a cat to have a cat, then *bam* they have a cat. It just doesn't necessarily have any kind of effect on any rolls. If they want it to affect structured encounters in some way, they can usually be represented as an ability for the player such as giving them a boost die in certain situations. You could also allow the pet to fetch an item in narrative encounters.

I don't have all my books with me at the moment, but i follow the guidelines in the back of the Force and Destiny book. It has a section about making "juvenile" versions of animals in the book (for jedi that take the animal companion takent). So for say..... a cat i would just look at the feline monster and dial back the stats and abilities.

Otherwise; as said above it may not need stats.

It seems like no matter what game and what system I play, someone wants a party pet. But rarely do they want it for any sort of mechanical advantage. So I usually just handle it completely narratively.

i have found the Goon Rules quiet satisfactory for my players

https://community.fantasyflightgames.com/topic/265113-genesys-master-resources-list/

Personally, if the player spends some sort of resource then I'll have a commensurate effect in game; the more they spend the greater the impact the companion would be. Most likely the thing I'd do is to provide an "ability" or equivalent with a boost die in certain situations (as drainsmith said above). If it was an animal with sil 1 or more, I'd start to flesh out some permanent stats and that's about it.

Depends on if the player has the Animal Companion talent or if they simply just want a fur baby.

Warhammer FFG had companion rules if you want to find them for some detailed suggestions. They revolved around a companion boosting your own abilities. So, a War Dog might be able to Distract (Setback when attacking you), while adding a Bonus when you are attacking. A trained Eagle might give you Bonus to Perception checks. That sort of thing. The philosophy was to keep the PC rolling for himself and not adding another NPC to the group.