First of all, we all have to recognize that most people put on strength and muscle more slowly with calisthenics movements compared to weights. I love calisthenics and gymnastic strength training, but weights are just more variable to one's needs, and are easier to create the right resistance, especially for strong muscle groups like the posterior chain. So recognize that your choice of training method is handicapping your progress to some degree.
That said, an adult man can reasonably expect to see much better results by doing pull-up training three times a week. The idea that a 28-year-old should reasonably expect to be over-training with a few pull-ups and push-ups 3x a week is laughable. But it's true, you do seem to be over-training. It's not good to experience over-training symptoms from such a small stimulus after such a long time to acclimate to training.
Which brings me to your second self-imposed handicap:
Diet: Plant based.
This is why I asked about your diet. It's uncanny how often someone describes a failure to respond to training, and only reveals that they're vegan after I guess to myself. No vegan has ever liked hearing this. Nevertheless.
I have a lot of sympathy for animal welfare, and I consider it a moral imperative to minimize torture of animals in one's choices. And that's what CAFOs and other industrial animal products are: torture of animals that feel pain. That's why I go out of my way (and spend more money) to eat, as much as possible, eggs from well-treated hens, milk and yogurt from well-treated pastured cows, and meat from animals living as close to their natural lifestyle as possible, butchered as humanely as possible.
If you want to go several extreme steps further, that's your choice. But I think it's important to recognize that very, very few people are able to make serious strength gains on a vegan diet without the aid of exogenous hormones (steroids). I suspect that if you started eating six eggs from well-treated hens a day, you would feel better in your workouts and see noticeably better strength progress. If on top of that, every day you ate a quart of yogurt and a steak from pastured cows, I'm pretty sure you'd see your training turn around. The power of eating animal foods for physical well-being has been well-understood for literal millennia.
If you're okay that your diet interferes with your physical health, okay. But you should at least know the choice you're making. I think the negative physical consequences of not eating at least farm eggs--which I find quite difficult to argue against from an ethical perspective--are in fact quite more serious than many vegans seem to reckon with.
