short story: he's signed to 300, which is under Atlantic. he is also still contractually obligated to 1017, but they dont operate as a label for him currently, they just take a check (if there is any checks being written). he was never signed to Cash Money, he's just managed by Birdman.
long story:
when Gucci got locked Thugger thought his contract with 1017 was voided (stupidly), & he signed a terrible SECOND contract to APG / Artist Publishing Group. They helped push 'Stoner' to some success, but the business relationship soured quick, they wanted to stay focused on pushing 'Stoner' -- and got mad at the 'Danny Glover' leak. Thugger felt they were holding him back & refused to work with them, & then they basically just stalemated back.
APG is a small boutique publishing company run by Mike Caren, whom in his more significant day job is President of A&R for all of Warner Music Group's labels, including Atlantic Records and Warner Bros. Lyor Cohen had just started 300 under Atlantic, & convinced Caren to transfer his APG contract to 300, without even really consulting with Thug.
Thug wasnt very receptive of his new position with 300, & they hadn't proven themselves at all yet. Thug wanted Cash Money to buy out his contract, but Lyor wouldnt sell, so Birdman just became his manager instead. Cash Money released some material under the name Rich Gang (with Young Thug considered as a "guest appearance"). As far as I know they technically only released 'Lifestyle' & 'Take Kare', with the rest of his Rich Gang material never "officially" released.
300/Lyor didnt cockblock his creativity with Rich Gang, since it was ostensibly helping brand their artist, & they've slowly won Thug over after establishing themselves with Migos success. The Barter 6 album was originally just going to be another free mixtape, but they convinced him to let them release it officially. They helped with his touring. & Now, with the recent sorta crumbling of Rich Gang/Cash Money, they have a wider opportunity for a even better working relationship, shifting the focus towards his 'debut' Hy!£UN35. (who knows if 300 can release a successful "album" tho -- they just failed pretty hard with Migos)
But he is still signed to 1017 too though, which is currently independent, & pretty much dormant at the moment. But that'll change when Gucci gets out next year. Perhaps 1017 might get back to playing a role in his releases again, or maybe Gucci'll spazz out on everybody if he hasn't actually been getting his money. Who knows with Gucci.