There's some great info above and in the answers to your other thread. Your slower progress is something I noticed that happened with my son last summer and this summer. It may be related to the relatively low number of reps you can perform now. Maybe the volume isn't high enough. What I mean is it's hard to progress in chin ups if you can only do two. Band assist, negatives, and other techniques work for some and don't do much for others. Each workout may drift close to max out territory, especially if you use negatives, which may not be productive long term.
A few weeks ago my son switched to a GTG style with chin ups and push ups and has seen some new progress. I also have him doing the trap bar deadlift (TBDL) when he gets home from school.
You haven't provided a lot of details of the program that you're using or if you have any other equipment available. I bought relatively inexpensive trap bars from Amazon and a bunch of used plates from Craigslist. If you can get a trap bar and some used plates within your budget it could be a very useful tool for building full body strength. It's funny but true that a used plate weighs the same as a brand new plate, and lasts just as long too.
Maybe take a step back and completely simplify your training for a little while. If you can get a trap bar and plates, use it with a very simple linear progression workout 3 days per week. You don't need a bench, spotter, or safety rack. Do 3 sets of 5 reps of the trap bar deadlift (TBDL). Start somewhere in the 80% range of your 5RM. Add 5 lbs or 2.5 kg per workout. Rest 3-5 minutes between sets. Closer to 5 minutes as the weight goes up. Once you can no longer add 5 lbs or 2.5 kg take two days off and retest your max. Calculate 80% of your new max and start the program over again. At the end of your 3 sets TBDL do some farmers walks with the same trap bar. You may want to adjust the weight, lighter on some day for longer walks, heavier on other for shorter walks. For now, aim for 20, 30, or 40 second walks. Work up to a total of 2 minutes of accumulated time under tension across the farmers walks each workout. The TBDL and farmers walks will significantly strengthen your grip and your upper and lower back. They'll hit most of the rest of your body too. Build some real strength.
In addition to the above, use a laid back GTG approach with chin ups and pushups. For you it will be singles on the chins, and maybe just 2 reps on the pushups. In the evenings, every 15 - 30 minutes, do one perfect chin followed by 2 perfect push ups. Do these about 5 nights per week. Let you body dictate the nights off. Don't push to failure, not even close to failure. The rep speed on each rep should be smooth and consistent. If you have to strain or the rep starts to slow down, you're done for the evening with that exercise. If chins slow down before push ups or push ups slow down before chins, it's okay to keep GTG with the one exercise that hasn't slowed down to get some more volume. Listen to your body on these GTG exercises. If you get to the point where you're doing 10 or more GTG sets per night, take a night off and then re-test your max for each exercise. Let us know your new max when that happens.
It's obvious from your posts that some frustration is setting in. You're working hard for little return on investment. What I recommend above will take very little time commitment and maybe by simplifying your workouts to just these four movements you can kick start your progress again. Give it a solid 100 days test drive. Resist the temptation to add other exercises except for a brisk walk after dinner and see if it works.