We see the Ring of Power turns Gollum and Bilbo and Frodo invisible, but is that what it would have done for Boromir? For Gandalf? For Gimli or Galadriel? Almost certainly not.

It would turn the mortals invisible and the immortals it wouldn't.

Hobbits, Dwarves, Men would be rendered invisible. We see Hobbits and Isildur becoming invisible.

Gandalf and the Elves are immortals, they exist partially in the unseen world, just like Sauron. This seems to prevent the ring from shifting the wearer completely to the unseen world.

The ring wraiths have worn their rings so long they passed into the unseen world permanently and can only be seen by their cloaks. But Frodo can see them with the ring on.

My interpretation would be that the ring basically takes your position on the scale of "seen world" to "unseen world" and flips it - those previously fully anchored in the seen world will be sent to the unseen world, and those that exist in both will still exist in both. That includes Maiar like Sauron and Gandalf, and the elves.

We saw in a flashback what it could do on Sauron's finger, and the only thing it did for Isildur is quicken his death.

He became invisible. That wasn't just a film adaptation thing, that's in Tolkien's writings too.