Depends on how you define “strength and muscle gains”.
Like, if you only did cleans a few days a week, you’d get very strong (on cleans, on most pulling exercises, and probably on most leg exercises) and you’d build muscle (primarily in the back, traps, shoulders, and legs).
For more “complete” development, a squat, some kind of pull, and some kind of press 2-3 days a week are probably the bare minimum. Whether that’s the original 20-rep squat routine (1x20 squats with BTN press and pullovers as assistance work), the old school 5x5 with bench-squat-dead or bench-squat-power clean, whatever.
To be fair, you’ve been asking about minimal training for a year and a half. Your first thread on the site talked about training two days a week every other week, along with other threads about minimalist training and very short workouts.
Is your schedule that jam-packed or, being honest with yourself, do you just not like lifting?
You mentioned intensity and volume, but not frequency. Those are the three variables to balance for results and recovery. Dan John has a program that’s high frequency, low volume, low to moderate intensity.