That’s a common phenomena.
I read an interview with Dan Blocker (who played Hoss Cartwright in Bonanza) years ago where he related an interaction he had with an older lady somewhere in LaLa land where he lived and she engaged him in a conversation about his family, life on the ranch, asked how (named characters) were doing and to give his best to his Pa from her.
He hadn’t known this was a thing.
The movie Galaxy Quest had fun playing with this concept, with young “Trekkie”-like adolescent geekazoids were - in their heart of hearts - convinced the show was based on reality only to find out that yes, it was.
The way I know things on TV are only play acting is, when I turn off the TV, I can’t find references to any of the things on it elsewhere - if I avoid tabloids at the grocer’s checkout stands or entertainment section of the local paper.
The same thing happened with Mark Hamill....Luke from “Star Wars.”
Before that, Hamill was on a soap opera.
He mentioned on a talk show years ago that a woman approached him in a supermarket and said, Did you know your best friend is doing this or that behind your back, and your girlfriend is doing this and that, and similar stuff.
She thought his soap character was real!
Hamill just said, I didn’t know that! Thank-you for letting me know. He just played along.