How do you actually increase your bench press?
Some people would recommend the Face Pull exercise using the rope attachment on a pulley weight machine. This is a good exercise, but you will not be able to load it to much more than 150+ pounds.
The answer to this problem of how to increase your horizontal pulling strength is to load the movement into the 225-250+ pound range. If you want to do 10×225 Bench Press, then you will need to be able to do roughly the same weight and volume combination in the opposite direction. Same idea applies to squats paired with RDLs.
I recommend using the EZ Curl Bar for the Bent Over Row exercise with the goal of increasing Bench Press strength. The EZ bar is about 25 pounds. You can load your 45s or 35s on there and clip them on just like a barbell. The rotated grips on the bar allow you to tuck your elbows in close to your body, so you can pull with more speed and power. Building up this speed and power in the Bent Over Row exercise will DRAMATICALLY increase your Bench Press strength.
After years of trying various ways to get my Bench Press to be better, I finally figured out the EZ bar idea during Covid.
I hope you can use this advice to increase your Bench Press!
Also, I think pull ups do basically nothing to make you stronger in Bench Press. Bent Over Row is the important lift to do.