I am trying to incorporate Hip Hinge into my training because I am realizing that Bodyweight training is leaving a huge hole in my strength because there is no hinging.
I am mostly a calisthenics guy too. The only "hole" I see in calisthenics is that there is no deadlift. But if you are training your back, and training your hips (see below) then I think you are fine.
One thing to consider is that if you are interested in calisthenics and you feel good.....then why care so much about a hinge? If you can do pistols for reps, jumping, lunges, etc, and you can lift what you need in day-to-day life, then who cares? Imo the supposed negative effects of "strength imbalances" are wildly exaggerated. On this note, another thing to consider is that you can do your hinge work like once or twice a week and that can be enough. I want a 90 degree pushup some day, so I don't want huge legs either. So I just train squats with low reps and high weight.
So if you want a strong hinge/legs, look into the low rep, lower frequency version of Easy Strength. That is, do very high weight, for 2-3 sets of 2-3 reps, 2-3 times a week, MAX. You can build strength but you certainly won't build a lot a muscle. Just because kettlebells are popular here doesn't mean you have to do swings all the time. If you like them, then try what was suggested and let's see if we can make them work better for what you want.
If you are worried about your back specifically, do back lever training, any kind of planche training (bent arm planches require the back to isometrically contract as well), reverse hypers off a block (see below), and do arch rocks. Then do the hinge drills I posted, and the one below.
Seriously, try those drills I posted. Then try the kickstand hinge. They will teach you how to hinge at the hips better. I never felt my glutes and hamstrings working so hard with
just body weight. Try each for three sets of ten. You will feel it. I did three sets of ten for the first time and I had a hard time walking the next day. Between the kickstand hinge, hindu squats, and some low rep front squats and deadlifts, I am plenty happy with leg and hinge training.
This demo has pretty good cues. You can also check out David Grey's info on the kickstand hinge (search "David Grey rehab" on instagram/interwebs). He has awesome content.