@alidvx So you really gotta try as hard as you can to take the shame out of struggling, because there should be no shame at all in struggling to do modified pushups. Even super duper modified ones! Your body is built in such a way that it makes it harder for you than it does for others. I've been powerlifting for 10 years and I can't do a bodyweight squat without special shoes. Bodies are weird, and you can't get down on yourself because your body is built in such a way to make it harder for you. That's not you failing or being bad at stuff, that's stuff coming harder for you.
So that said, practical techniques, I think my FAVORITE tip for getting better at pushups and other bodyweight activities is the controlled negative or the "seal up". You found that you can't do a wall push up in the position you tried it. But, for example, I bet if you put your feet like 6 inches away from the wall so you're standing straight up, you could do it then right? There's some position you can put yourself in where you can push with your arms and feel some resistance but you don't fall down. The struggle is, you gotta find a position in between "I feel like I could just push my hands at the air forever" and "I can not even do one push up like this". So one thing that I think helps a lot to change it up and transition from "just push on the wall a bit" to genuine wall push-ups, is to start the pushup in the harder wall-push-up form that you can't do, and lower your body to the wall. Then when you're at the bottom, step your feet in, and push up the easier way. Lower the hard way, push up the easy way.
It works for any go between of push-up skills. If you can almost do pushups on the counter, lower yourself slowly to the counter, bring your feet in, push up, repeat. If you almost have knee push-ups, get in knee-push-up form, slowly lower yourself to the ground, use child pose to get back up, repeat. If you have knee push ups but not full push ups, lower yourself in a full pushup, leave your knees on the ground, do a knee push up, pick up your butt. It helps because you're using all the muscle groups of the harder pushups, but it's easier, so you can crank out more of them.