I moved to California from Massachusetts with a buddy 30 years ago. In about 2 weeks I sounded like a native. I made no conscience effort to do so; I just slipped into it. My friend, despite living there all these years, still speaks with a distinct Boston accent. It’s weird.
Its probably different depending no the person. You went from a US state to a different US state so there was no language acquisition with you which may partially be responsible for your easy transition between languages. Schwarzenegger and I have different native languages which may impact our accent in english
This gets my Gf into trouble as she can land up imitating the Indain accents of people she has being working with at which poiont they think she's being racist so has to make a concious effort not to.