Shoulder press

So I have decided I want to integrate a shoulder day into my weekly schedule, due to my delts currently getting no direct work.

The problem: I bench press twice a week with the goal of strength gain. One day is my primary day, where I usually do one rep of incline at rpe 8-9, followed by backdown sets. Two or three days later, I’ll do flat bench for 7-10 reps. This is usually done at rpe 6-7. I like this schedule because there is a good amount of frequency, but I still have time to recover from each session.

I am wondering if there is a way I can integrate a shoulder day without sacrificing progressive overload/strength gain on my bench? I am also interested in growing a strong standing barbell press if possible.

How much frequency and volume can the triceps take and still gain strength on compounds?

Would it be better to spread shoulder workout sets throughout the week, as opposed to a specific shoulder day?