Physical Education

The important thing is to find ways to progress from workout to workout. If you're capping out at 2 sets of 28, then switch it up. Break up your target total reps and do more sets with less reps (If you're aiming for 60 push-ups for the day, try doing 4 sets of 15 instead).

For muscle growth, general rule of thumb is that you wanna rest at least a day before your next workout targeting a major muscle group (in the case of pushups, it's chest/triceps). Same for strength programming.

However, given that you are still in the "noob gain" phase of strength fitness, you got a lot more room for progression no matter what your routine is, as long as you are consistently working out. Unless you're doing hundreds a day, push-ups with good form (important!) are also pretty easy on your body compared to other exercises and you should be able to get away with doing them as frequently as you want. You could do them 7 days a week and repeat.

My advice, find a beginner calisthenics programs and do your best to stick to that for a few months. That's gonna give you a solid foundation of strength, endurance, and mobility for when you eventually get the desire to branch out to other programming.

Credentials: Not a fitness expert by any means, but I have consistently been doing powerlifting workouts for over a decade and have gone through several programs, bodyweight programming included.