There are 2 issues here, both important. You are asking about one of them, and people are answering about both, so it may com across as confusing. You are asking about the number of exercises, and people have added comments about the organization of your training, your "template", though they haven't used that word.
The idea that you need 1 exercise for every muscle group will lead you to insanity. There are too many muscle groups. But there's hope. If you rely mostly on compound exercises (which you do to some extent if your push day is representative), you will work lots of muscle groups with only a few exercises. There may be good reasons to use isolation exercises at times (moves that work only one muscle), but they are of much less importance. So for instance, you squat, so you don't need leg press or the abductor machine. You might use these sometimes, but they aren't part of the heart and soul of your training. You have BB bench press. The DB incline press is a fine exercise, but it will probably be something that you put in from time to time as an "accessory" lift.
We have a habit here of answering questions that weren't asked. Sometimes that frustrates the poster, who isn't getting a clear answer to what he or she thought was the important question, but people with experience see issues that are often bigger than what the poster is asking. That's why everyone immediately started dissecting your split.
It will be easier and simpler for you if you stop trying to think through every muscle group, and think about movement. There are 6 basic movements, and if you cover them with roughly equal emphasis, you will have pretty balanced training, and your workouts won't be too terribly long.
Vertical push (i.e. press)
Vertical pull (i.e. chinups, etc.)
Horizontal push (i.e. bench, etc.)
Horizontal pull (rowing, etc.)
Hip dominant lower body/posterior chain (i.e., deadlift)
Knee dominant lower (i.e., squat)
Dumbbell Bench press
Leg press (machine, not sled)
Dumbbell incl bench
Hip abductor (machine)
Overhead tricep press
So, if you dropped everything except the squat and a bench press, you'd have time for an overhead press, and you could be out of the gym in an hour. On your other day you could deadlift, do some sort of row, and some chinups, and again be out in an hour, and you'd have a pretty balanced routine. But I know how people are, you'll want to put in a few other lifts. Fine, if you have time. Pick 1 or 2 to include for a few weeks at a time, or even very them every workout. Don't go real heavy with these. If you hit your main lifts hard you won't have the energy to anyway.
Do the biggest lifts first, i.e., the one that uses the most muscle. Do any isolation moves last.
Good luck, and welcome to the forum.