We have several rehomed cats, and one we rehomed several years ago came to us as a 'biter' - he was only 10 months old, and had been picked up as a stray so his manners were less than perfect!
We learned pretty quickly that he gets over-stimulated. Loved to be on someone's lap and petted, but only until he was 'all touched out'. At that point he would bite to say 'enough'. So it's important to learn your cat's signs for when enough stimulation is enough for them.
Loads of people have mentioned jute mats - they're excellent. We have several scattered around on various floors, as well as several cat trees upstairs and downstairs (not all cats like to scratch on a post, just as not all cats like to scratch on the floor) so they have a choice according to their preferences!
We had a furniture scratcher who came to us as an adult cat, and found that the double-sided cat tape worked well on the furniture - they don't like their paws on something sticky, so if you put the tape in the places where you can see they like to scratch that will put them off (but you have to provide alternative - cat-suitable - places, obviously!).
We also had a lot of success 'clicker-training' one of our cats to stop scratching the furniture. People think you can't do it with cats, but you can. But I won't lie - it was a lot of hard work because you have to encourage scratching in the right place/click/reward every time they get it right. I ended up with pockets full of cat treats and the clicker round my neck while trying to wfh! But it did work, so it's an option if you have the tine to put into it if nothing else works.
Cats are the best, aren't they! 