Does your diverticulum cause a vesicocele? If the diverticulum is the only cause of your inability to urinate on your own, removing it will most likely alleviate you of this problem. If the diverticulum is not the sole cause, then at least the will be much less or no residual urine and less probability for an UTI. If you are not sure how to decide, I would suggest you get a second opinion from a specialist. We dont know you and cant give you a definite, well funded suggestion.
Inability to empty the bladder can be caused by a number of things - usually there’s an obstruction of some type. The diverticulum could cause an obstruction. Other causes could be nerve issues - I have what’s called a neurogenic bladder, which means the nerves in my bladder are damaged, causing inability to completely empty my bladder. I do not cath though - it simply takes me longer to go to the bathroom.
I agree that more information would be helpful, such as how long you’ve been cathing. Using a catheter on a daily basis can cause UTI, as can urinary retention. Can you urinate on your own at all?
I think more info would be helpful, as a bladder infection should be curable. Usually, the inability to empty the bladder is due to a structural or other problem, not an infection unless I suppose if the infection has been there undetected for so long it caused irreversible damage. But again, the treatment for a UTI is to cure it, and then it's gone. So again, more info might get a better answer from someone.