This question is for dhergert, but others are welcome to weigh in. Are there certain pizzicato techniques or approaches that you think would help reduce tension/pain in the wrist? Similarly, are there strings that you would suggest that help with this problem?
I have been using the Evah’s light gauge for a few years. In the past I used spirocores-medium gauge.
There are players here with decades and even half-centuries more experience than I who can and are answering this so I'd definitely listen to their advice as far as particulars are concerned...
Personally for straight pizz I use index and middle fingers (sides) together, with the thumb anchored on the bass-edge of the fingerboard, as much as possible so I'm not over-powering a single finger all the time. I will use those two fingers separately for short fast passages but only as needed. I do a light-slap (triplets and quads) for roots and bluegrass and for that I try not to overuse my wrist swivel movement, keeping it subtle and relaxed.
I have had trouble in the past with nerve issues in my neck, lower back, wrists and forearms and have spent months in physical therapy multiple times in the past for those issues, so I try to maintain proper posture and try to keep my wrists and my arms and elbows as straight and as relaxed possible. And as I'm getting older (65) my hands take longer to get moving (arthritis) so I go out of my way to soak them in very warm water (washing dishes!) which does help. If I do get hand injuries (cuts, bruises, blisters, strains), ice is one of my primary solutions.
As I mentioned about variety of movement, I routinely change-up what I'm doing between various pizz and slap techniques and locations on the neck and fingerboard, so my hands and wrists and forearms get a good range of activity. I do practice arco every day even though I rarely use it in public, and I always bring a relatively [un]comfortable adjustable height playing stool and [gladly] alternate between various elevations, sitting and standing while playing.
While I'm only 15 months into double bass, I've played other instruments professionally for about 50 years and I'm extremely protective about continuing to play those instruments. So I am using very low tension synthetic non-metal strings (Innovation SilverSlaps EA, SBW Deluxe "Dirty Guts" DG) and I expect to continue in that direction although I may eventually move into guts for D and G. Thicker strings feel better in my hands.
I fully endorse mentors and teachers, but when it comes to possible nerve pain and various injuries, I'm sure if you ask your mentors and teachers if they will be liable for your health, they'll say no. I'd encourage you to seek out proper medical care if you are dealing with anything that is keeping you from enjoying your music. My cumulative years of experience with DPTs and PTs has been excellent and I can highly recommend them for this kind of problem.