Bodyweight progression?

I've been training for about 5-6 years now (though mostly just basic stuff like push-ups, dips, pull-ups, lat raises, leg raises, crunches etc) and now I feel like I've hit the limit when it comes to push exercises.

I can do about 35-40 dips in a row (I'm 178cm, 72kg but I was able to do similar number of reps when I was 82kg). I can do over 60 regular push-ups and about 40 diamond push-ups. I'm afraid of levitating (statics) as I feel my core isn't as developed. I'm pretty sure I can do handstand push-up assist but I just don't have good places to train (and I'm also afraid of hurting my lower back lol). I am aware anything above 20 reps is just doing cardio so I definitely want to reduce that. Any tips on I should do? I can do about 30-40 leg raises and similar number of crunches so I'd say my core is decent but definitely not the best. I basically feel like I don't have any control when I try to do handstand push-ups. As for my shoulders I can do about 12-15 reps of lat raises with 8kg kettlebells so I'd say I'm good on that part too.

The only issues I can see with my progression are: pull exercises (can barely do 6 clean pull-ups), back (especially lower back), core. Any tips are more than welcome, thanks!