AFAIK Coinbase was the repository holding company.
Tbh I think the way it works is almost fractional share accounting, and they just "show" the numbers when required, but circulate the same coins
Discussion
If you are a normie company that hold some Bitcoin and trust Coinbase to hold them for you, then so be it.
But if you are a Bitcoin company, trusting a third party to hold your coins is not the best strategy.
I would say that they probably have to use a third party custodian, but then again, Fidelity custodies for their own ETF.