It has stuck with me immensely. I haven't watched it since about a year ago, and it is still resonating with me. I don't remember being entirely invested in it, but I remember a ton of details from it. I'll wake up sometimes remembering images from this film, very few movies have caused me to do this.
Has anyone else had a similar situation with this film? Or others?
Goran,
Yes, this is one of my very favorite films, but it is the particular way that it resonates that fascinates me.
I don't only like "art" films. The way I enjoy a film like Lawrence of Arabia, for example, is very different than for this film. Or The Thin Red Line (which to be fair some would consider an art film even if a war/action film at the same time).
Persona is more about its themes than its narrative. One thing that is quite compelling about it is how despite that consideration it has so many great cinematic elements that as you say stick with you. Then there is its timeless style.
In addition to some other of Bergman films, I would say the experience I have had closest to what you describe with another director's film would be with Antonioni's L'Eclisse. If you are interested you might try that one. It is not similar in its subject matter other than being what I would call an existentialist film. But it has a similar fascination about it.