Back Muscles Training Exercises

Great to hear you're interested in strengthening your back muscles! Given your intermediate fitness level and focus on strength and flexibility, I have a few suggestions. Also, the available equipment and frequency are excellent for targeting different parts of the back.
Warm-Up (5 minutes)
Light aerobic exercise, like jogging in place or skipping rope
Strength Exercises (20 minutes)
Pull-Ups: 4 sets of 8-10 reps. Use your pull-up bar.
Band Rows: 4 sets of 12-15 reps. Use your resistance bands.
Face Pulls: 3 sets of 12 reps. Also use resistance bands for this.
Flexibility Exercises (5 minutes)
Child's Pose: Hold for 30 seconds to 1 minute
Cat-Cow Stretch: Perform 10 cycles
You mentioned lower back discomfort. It's important to listen to your body. Avoid exercises that make this discomfort worse. If the discomfort persists, consider consulting a healthcare professional.
You already do deadlifts and pull-ups in your current routine. These new exercises will complement them well. Since you prefer bodyweight exercises, pull-ups are a great fit. You can add variations like wide-grip or close-grip to keep it interesting.
Feel free to adjust the number of sets and reps according to your comfort. Make sure to cool down after the workout with some light stretching. Enjoy your training!