Add reps, then slow the tempo, then move to harder leverage variations before adding external weight.
The quick answer
With bodyweight training you overload by making the movement harder, not just by adding reps forever. First add reps within a range, then slow the tempo and add pauses, then progress to harder leverage variations, for example incline to standard to decline to archer push-ups. Once a movement gets easy at high reps, add external load with a weight vest, backpack, or dip belt to keep it in a strength-building range.
How to think about it
Progress the leverage
Bodyweight strength comes from harder variations, so climb a difficulty ladder: knee push-ups to full to feet-elevated to one-arm progressions, or rows to pull-ups to weighted pull-ups. Each step raises the effective resistance without any equipment.
Use tempo and pauses
When you cannot yet reach the next variation, slow the lowering to 3 to 5 seconds and add pauses at the hardest point. This increases time under tension and difficulty on the same movement.
Add external load eventually
If you are doing 20-plus clean reps, you are training endurance, not strength, so add weight to get back into a 5 to 12 rep zone. A weight vest, loaded backpack, or dip belt lets you keep overloading push-ups, pull-ups, dips, and squats.
Do this
Add reps in a rangeBuild reps within a target like 8 to 15 before advancing the exercise.
Progress the variationMove to a harder leverage version once the current one gets easy.
Slow the tempoAdd 3 to 5 second lowers and pauses to increase difficulty in place.
Load up when easyUse a vest, backpack, or dip belt once you exceed 15 to 20 reps.