Pets often help with mental health as long as caring for them is not an excessive burden such as financial, time, personality mismatch, et cetera. Cats are my favorite.

I'm very sorry for your loss and can definitely sympathize that grief can last a very long time.

In general, the advice I've heard is that yes, assuming finances and other circumstances permit, you should get another pet. It doesn't have to replace your previous cat whom you can still continue to love and remember fondly, but it'll be a new companion and pets help humans cope with life in a bewildering variety of ways.

With pets you also don't have to worry as much if you're still processing some emotions. For example, if you rushed into another relationship with a human partner but still hadn't processed the emotions from your previous partner, you're bound to cause some confusion and hurt feelings for both of you, but this doesn't apply to pets as long as you love and care for them.

Take some time, find a cat you really click with, and enjoy your new companion.

Edit: and yes, pets most definitely help with mental health.

My cats are great. One will snuggle with my face so I can’t breathe while the other attacks my feet. That way I don’t over sleep, lol. They are great though. They always want attention and great me at the door when I come home. Littermaid self cleaning cat box makes things much easier. Make sure to get the corn cob litter if you get one.

My animals give me purpose in life, so I'd certainly say they improve mental health!

It is currently kitten season - that time of year when shelters are overflowing with kittens. You could volunteer to help socialize new kittens at the shelters if you're unsure about adopting.

Cats are wonderful. Except when they leap on you when you are dozing on the couch, because your only purpose is to be their pillow.

You have to earn their companionship which makes it more valuable.