I can't be sure at 100% of course, but they have chosen to stay independent. With this AAA game planned to be a sucess and Kojima himself, I think his studio will have enough traction to deal with financials and publishers independently... like they did with Sony.
Kojima said he plans Death Stranding to become a big franchise beeing the pillarstone of the studio.
Without Sony there is no Death Stranding 2
Apart from that he is benefeting strongly by working together with Sony, something he wouldn't have at most other publishers.
He got the creative freedom and AAA Budget for a Game, that i can't think many other publisher would be willing to fund.
He is working with a Sony Engine and is even helping to improve it - if he works with another publisher, he would have to start from zero again and find or even build a new Engine.
Apart from that he is also getting support from Sony and its Team (Tech, Engine, MoCap)
I don't see Kojima switching publishers and basically start from Zero again after this Project. This is the start of a longterm parternship.
Of course that doesn't mean, that he only works with Sony. He could work on small projects for other Publishers