I've heard stereotypes but does anyone have first hand experience with how they were treated as foreign residents in Japan?
The concrete daily-life answer is, I've virtually always found it an incredibly welcoming place. With very few occasional bits of garden-variety discrimination ("oh sorry this apartment isn't available for rent to foreigners"). But individuals are nearly always nice - obviously polite, but usually nice as well. And society in general is far more accommodating to foreigners than one might expect a society to be to ~2% of its population (putting English on road signs and so forth).
But over the years I've noticed that lots of people online are super confident that Japan is deeply racist, which is wildly at odds with my experiences here, so I've thought a lot about where that comes from. And personally my view is that racism, as the term is generally used, isn't a meaningful thing to talk about with respect to Japan. The Japanese (broadly, oversimplifying) don't see the world in terms of race - they divide the world into Japanese and non-Japanese, and things like skin color or nationality are very distant lesser concerns. And in general, they don't at all see Japanese things as better than non - Japan is mostly fascinated with foreign things, and in many contexts looks up to them as superior to local ways.
But Japan does always, always see non-Japanese things as other, and separate. And as such people are often quick to, say, attribute differences of opinion to "oh I guess that's how foreigners see this, but I'm Japanese so I see it differently", and such. And when one is on the receiving end of that, and constantly treated as separate, it can feel like racism (though I think it's misleading to model it that way).
Oh, last thing to add is that regardless of how they see or treat foreigners, the median Japanese person nearly always harbors some level of dread at the thought of talking to a foreigner, since that means using English. ~Every Japanese adult took 6-10 years of English in school, and in most cases they are almost entirely unable to use it in conversation for various reasons, so many people here view using English the way I'd feel about suddenly being given a quiz in my worst subject from high school. As such, tourists who go around using English may mistake people's reactions for standoffishness or hostility - but if you live here and learn even the most absolute basic Japanese, you find everyone melts and things go fine.
What would you say the governments posture toward easing immigration looks like?
That being said, it does come with it's own share of “foreigners not allowed or welcome” experiences. There’s also racial undertones to those experiences, where some set of people will have worse experience than others.
Real racism in Japan is about Chinese and Koreans. Non-Asians make up less than 1% and just aren’t relevant, e.g. racist parties never talk about them in speaker announcements from busses.