The question of ownership rarely comes up while a project is going well. It comes up two years later, when a business wants to move to a different studio, or the original developer stops answering email, and discovers that the pieces of its own website are scattered across accounts nobody has the password to.
There are five things to hold. The domain name should be registered to your business, in an account you can log into. The hosting should be billed to you. The code should sit in a repository you control. The analytics property should be yours. And the content, meaning your words and your photographs, should exist somewhere other than inside the site itself.
The common failure is not malice, it is convenience. It is genuinely faster for an agency to register the domain on its own account during a build, and then simply never move it. The result is the same either way: a business that cannot leave.
The test is simple, and worth applying to any studio including this one. Ask what would happen if you wanted to move everything to another agency next month. A good answer is a short list of accounts to transfer. A bad answer involves the words "well, it is a bit more complicated than that".