I only own The Players handbook on Dndbeyond, but I noticed when I make a fighter, ranger, or paladin I can sometimes select the new fighting styles from Tasha's Cauldron of Everything. I noticed that I can only select these fighting styles after 3rd level, and only with certain subclasses.

If I select Battle Master or Eldritch Knight for fighter, I have access to these fighting styles, but if I choose Champion I do not. If I select Beast Master for ranger I have access to these fighting styles, but if I choose Hunter I do not. If I select Oath of the Ancients or Vengence for paladin I have access to these fighting styles, but if I choose Oath of Devotion I do not. I have noticed that the subclasses where I can use these fighting styles are the ones from the Players Handbook, and the subclasses where I can't are from the Basic Rules.

I am not sure If I am supposed to have access to these fighting styles, (as again, I have not purchased TCoE) but I would be surprised if they are meant to be locked behind certain subclasses.

Hope this helps

Are any of the characters who CAN select the new fighting styles in campaigns with content sharing turned on? If yes, then I'd bet that someone in those campaigns have TCoE.

No, they aren't. One of them is a character that I'm actually playing, but I made the rest strictly just to test out how to get access to these fighting styles. I don't even use content sharing or campaigns on dndbeyond.

Gotcha. And on testing with a Battle Master (I don't own TCoE either), I'm also seeing the additional fighting styles. And also the new maneuvers.