Bluesky was an initiative launched by Jack Dorsey while he was CEO of Twitter, and it was intended to develop a set of federated social media protocols and eventually move Twitter to those protocols. (https://www.cnbc.com/2019/12/11/twitter-ceo-jack-dorsey-anno...)
He hired a development team for it (led by Jay Graber) who still work on the project today, probably as employees of Twitter? Jack's role in the project is unclear, apart from being a board member of the organization.
I have no idea what the relations between all the parties are at the moment, considering Dorsey x Twitter x Musk x everything else that has happened since December 2019, but as far as I can tell Bluesky – while working independently – is still fully funded by Twitter. It is not Dorsey's company as everyone seems to believe.