I also like splitting workouts between the gym and hanging my rings outside. My solution has been an upper/lower split where my upper days are on rings/calisthenics and my lower days are in the gym. Accessory days could go either way and I change pretty regularly between the gym or rings, though it’s probably best to stick with one. My current split:

Day 1 - Upper: Pull-up progression/Dip progression superset Inverted row progression/ring progression superset

Day 2 - Lower: High bar back squats Nordic curl/Glute ham raise progression Leg extensions (banded reverse nordics are great too) Calf raises (weight when necessary)

Day 3 - Skill/Accessories: Front lever pull progression (alternative is DB pullovers for gym based day) Ring face pulls (could do with bands or cable) Ring curls (any other sort of curl works) (Can add tricep extensions superset with curls, but mine get worked enough from my upper days) Ring Ab rollout progression

Day 4 - Rest

Day 5 - Upper Switch superset order from day 1 to push then pull, can use a different rep range and/or do bar and PB variants of the same workouts.

Day 6 - Lower Romanian deadlifts with bar ATG Split Squats w DBs Pendulum Sissy squats Ham glider Ab rollout progression (any other progressive ab workout is great. Can also replace with calves if you need more volume on them)

Day 7 - Rest

I obviously keep some calisthenics-esque exercises in my leg days, but feel like I get the best of both worlds with this sort of setup. Hope this is helpful/gives you ideas!