TLDR:
Use a handcrank machine!
My DD bought me a leather skin for my birthday, it’s beautifully soft and supple.
Do you know what type of skin it is, how it was processed, and what it's thickness is?
Different skins have different properties and thus are used for different products. Just as you wouldn't use hessian for lingerie, you wouldn't use bridal leather for a handbag. I have a couple of un-dyed pigskins which are as you describe.
The softest, most pliable leathers, tend to be chrome tanned. Tougher leathers are veg tanned.
I want to eventually make a small handbag but will start on something smaller like a card wallet.
Have a look at the videos uploaded by these two leatherworkers:
https://www.youtube.com/c/at%C3%B6lyederi/https://www.youtube.com/c/bitchen/Bitchen makes some of his patterns available free of charge; I use his wallet and purse templates as they are, in my opinion, the best designs.
Most of the patterns I look at are for fabric, I assume I treat the leather as I would a piece of fabric but don’t need to consider grain etc.
Yes, and no.
Yes, there's no grain to consider. But no, you can't treat it quite the same as fabric. Leather is tough to sew. Most domestic machines will cope with thinner leathers, but they rely on speed for penetrating power. I prefer to sew leather by hand, but if I were using a machine, I would use a vintage hand crank, purely because I would have far greater control over both the stitching and in feeding the leather under the needle.