Our cats are Covid cats, so are used to having someone around all day as DH works from home. Very rarely are they left "on their own" all day, but we do go away on holiday or for weekends away. They have a cat sitter during that time, but ultimately are left on their own for longer periods of time during the day.
One of the cats has a bit of separation anxiety and can overgroom. It's a bit like us biting our fingernails, so it's become like a habit to her. There's nothing "wrong" with her, but she can look a bit scraggy as a result!
The other one is perfectly fine without human company, but just makes up for the lack of it when we get home with lots of cuddles.
My old cat was used to having the house to herself. She was mostly an indoor cat as I didn't have a cat flap and she just used to sleep or play with her toys during the day. She never really seemed that put out that we weren't home.
Most cats are, therefore, pretty self resilient, especially if they have access to a cat flap.
If you are taking a cat over from a neighbour though, I'd recommend you keep it in for a good few weeks, so it can learn that this is its new home, or you might find that it just keeps returning to its old one anyway, but with you now responsible for paying all the vet bills!