How do you train hang board alongside climbing?

This autumn, I've decided to start taking my climbing seriously. I climb three days a week, Tuesdays, Thursdays, and Sundays for about 2–3 hours per session. Typically, I do two bouldering sessions and one rope session.

I tried increasing my climbing volume by adding another day, but I found that my recovery couldn’t keep up—I just ended up feeling beat. At the end of every other session, I usually do pull-ups on a hangboard with edges ranging from ~20–10mm, depending on how tired I am. I get around 7 pull-ups on the 10mm and 15 on the 20mm edge. I like to pull on edges rather than just hanging, as I feel this translates better to pulling on the wall, but I have no idea if this is true.

I’m curious to hear from strong climbers: how do you incorporate hangboarding at the gym and at home alongside your climbing to build strength?

• Should I do light hangs on rest days?
• Hang on the same day after my sessions?
• Or only hang if I miss a climbing session?

For context, I’ve been climbing on and off for about four years, but seriously for the past year. My current climbing level is 7a top rope and 7b boulder, and I'd like to just get stronger.