You might need to provide a little more information about what is actually wrong with your neck ( bone degeneration, bone spurs, problems with disks …etc. Can you turn your head, tilt etc without danger of injury? The advice to talk to a physical therapist who actually kayaks and paddles SUP is good, otherwise don’t put too much weight on what you get told, unless the therapist has good in depth knowledge about the kind of paddling you will be doing. That brings me to the other area you need to address. What kind of paddling ? Ocean and Coast, rivers with rapids, flatwater, lakes with wind?
If you are going to do simple paddling on flatwater a kayak would probably be easiest, unless you have issues lifting it and putting it on a vehicle, then SUP is hard to beat. SUP paddling is not very hard on the neck and likely if you can kayak you can SUP paddle too on flat water, it will strengthen your core and possible help with neck muscles. SUP helps to improve and maintain balance and flexibility, kayaking not so much. In waves and surf SUP surfing is much easier on the back and neck. I have some bone issues in the neck and back and I surf SUPs with no pain. Kayak and waveski surfing are much harder on the body.
One area where a kayak could be bad is rolling. Most rolls require good flexibility of the neck to keep your head close to the center axis of the boat when you roll up. SUP you simply pull yourself back on, so much easier to deal with falls /capsizes.