Foreigner is still used regularly without negative connotations. Foreigner is unfortunately also used with negative connotations. It all comes down to context and usage.
Some of that context is who you are as a speaker. If you are a xenophobic sort of person, or come from a xenophobic background or area, or if you fit the stereotype of a xenophobic person, the word foreigner is more likely to be heard with a negative connotation. Otherwise, it is less likely.
Of course, regardless of who you are, if you use the word foreigner in a negative way, the word itself will feel more negative. If you are a native inhabitant of the land you live in, and you are talking about people from other countries, you should be careful about how you use the word. I'm not saying it will always be negative in this context— in fact, it usually won't! Just be careful, as it's possible to use it negatively this way.
In the context you suggested, speaking as a person who moved from one country to another, the word "foreigner" absolutely does not have a negative context. It does have a connotation of loneliness, a connotation of feeling isolated and disconnected from the people around you, but I think these connotations fit the subject of the podcast you described quite well.