My training currently consists of calisthenic strength training 3-4 days a week on alternating days and HIIT (sprinting, cycling, heavy bag work) 2-3 times a week on non calisthenics days, with some yoga, bridges and headstands thrown in.
Should I keep my HIIT on non calisthenic days or do it on my calisthenic days (either post workout or later), leaving just yoga and inversions for the other days?
Either way will be fine, try both. I don’t often do cardio, but when I do its sprint intervals, usually superset with pistol squats (sprint, walk back, sprint again, but do a set of pistols on each leg between each sprint. High intensity cardio like that you can consider a type of strength training, and you could even consider sprinting and cycling to be forms of calisthenics (punching bag is more arguable, though I would still consider it a type of strength training as well). This means that doing these exercises on the same day as advanced calisthenics could exhaust you for the other workout. Overall if you do them the same day I’d recommend doing whichever is your focus in your first workout. So if calisthenics is your primary goal do that early and sprint later in the day.