You would be right if this is what expat was used for.
But now every immigrant from the UK, for example, refers to themselves as an expat, even if they’re working for a company local to the country they moved to.
Whereas in western countries we have “new Germans” or “new British” from all over the world.
They would argue that they don’t intend to stay forever in their new country so that makes them expats.
But like the post I replied to pointed out, someone from Bangladesh would not be called an expat but migrant worker. This is where class and social status gets mixed up in this as well.
I think they are both temporary immigrants.
To make it even more confusing, I know a few people who are ‘expats’ in their country of origin because they immigrated and then their employer moved them temporarily to their original country.