To progress quickly on high-intensity strength exercises like pull-ups, it is essential to significantly lengthen rest periods between sets (3 to 5 minutes) to allow for complete recovery.

noli's read

The community largely converges on the idea that long rest periods favor performance on high-intensity movements. Sports physiology research supports this approach: according to reviews such as the one by Schoenfeld et al. (meta-analysis), longer rest periods (more than 2-3 minutes) make it possible to maintain a higher total volume of repetitions throughout the session, which is a key factor in gaining strength. The post is based on a correct biological foundation regarding the renewal of immediate energy reserves (ATP-CP system), which indeed require a few minutes to be restored after maximal effort. The idea that low-repetition pull-ups are comparable to pure strength efforts (like powerlifting) is valid, because the central nervous system requires a longer recovery time than that for endurance exercises. It is, however, an exaggeration to say that rest is the only factor; total volume and load progression remain equally decisive. Finally, the use of assistance machines to increase work volume, mentioned in the comments, is a solid complementary strategy without invalidating the need for rest.

the sources

1. 1r/bodyweightfitness