What you have here is essentially just a list of exercises with no progression. It’s not really a program. Only being able to do a few sets of benchpress at a certain weight doesn’t mean that you can’t benchpress it means that you were not using an appropriate starting weight / progression. To failure isn’t really a progression plan

Here is some suggested reading: https://thefitness.wiki/routines/strength-training-muscle-building/

If you chose 531 for beginners for example, your 1 rep max for bench is about 120lbs, and your training max is just over 100lbs. Your first week of benchpress would look like this:

Main sets (65%, 75%, 85% of training max) :
70lbs x 5 reps
80lbs x 3 reps
90lbs x 1+ reps

Secondary sets (65% of training max):
70lbs x 5 reps
70lbs x 5 reps
70lbs x 5 reps
70lbs x 5 reps
70lbs x 5 reps

None of these reps should be grindy or shaky, The idea is to be training below your all out failure. After week three you would start the cycle again and increase the training max by 5lbs. This is a gradual progression that builds lots of experience with the lift and gives you plenty of time to adapt. You can essentially progress in this way for years, slow steady sub-max progression is the key to injury free success

The best thing you could do is to lower the weight. Aim for the desired rep ranges with good full range of motion, slower on the way down and faster on the way up. You'll hit that 90 for reps sooner than you think. If you really want to stick with 90, try adding a extra minute or two or rest before the third set.

Id strongly encourage you to do a quick warm up. Spike your heart rate just a little and do a few quick light sets of which ever movement you're starting with, building up the weight with each warm up set. This can be super important for avoiding all sorts of injuries, especially as the weights increase.

glx-gears --info
Hold on, I think I've misunderstood something here

Pick a weight your muscle can handle and leave the ego the entrance of the gym. If you pick a weight you can't do to completion for all your sets on the first day of the program, you picked the wrong weight.

Progression should be defined by any serious training program, if it doesn't have one, I'd question the competence of whoever published the program.

A common way to progress is to add weight after hitting x amount of reps for y amount of sets, but there are multiple ways to progress. You might want to add sets as your body adapt to the workload. You might increment weight after hitting x reps on your first set, ignoring how many reps you get on the following sets as fatigue kicks in. For women, incrementing the target rep instead of weight is also a thing.