About 5ft 7. I am, in all honesty, a very solid person. 8 years of religious weightlifting, and years of rugby before that. Just a dense mofo.
You’ll be totally fine. Unless you want to be a world class climber, you can get up some very challenging, engaging, and/or just plain fun stuff at a gym and outside with your build. Strength will be really helpful but it’s a lot of technique, flexibility, and muscles that you don’t use in a lot of other scenarios.
I'm no climbing expert, but i've once seen a beginner (as in never climbed in her life) lady absolutely brute force up a wall and leave all other beginners in the dust - looking like an absolute beast stuck to the wall all muscles engaged the whole way. It was impressive. Climbing is lots of technique actually so while strength and flexibility are a factor, i feel anyone generally fit can get a start. The easier routes are almost just going up a ladder type exercises.