My suspicion would be that it's tricky to study the effect of caffeine on strength training and strength performance because:

(a) in modern western societies it's difficult to find many athletic subjects available for studies who do not already have significant caffeine tolerance.
(partly because so many athletes took note of the earlier successful findings for caffeine in aerobic endurance performance - or just from heavy marketing of "energy" drinks).

. (perhaps caffeine was not studied earlier for strength-training because there were other chemicals with obvious greater effect for that).

(b) Strength performance has perhaps a larger neural/mental aspect. At a lower level there's "neural recruitment". At a higher level there's overall "psych" factor.
Like for aerobic performances I've heard that the difference between public time-trial speeds and private/personal time-trial speeds are only about 3 percent.

So it's possible that some athletes for strength training have found ways to increase mobilization of neural/mental resources other than caffeine, so taking a caffeine pill doesn't make much difference. While athletes inexperienced with pure-strength performance (and who do not otherwise drink caffeine) might get a significant caffeine boost.

I'd guess caffeine might help for some climbers in some performance situations, but not for many others.

Ken