Is it permissible to seek immigration, residency, and employment in foreign countries, and does this contradict the Hadith: "I am innocent of any Muslim who resides among the polytheists"?

Immigration to lands of disbelief is not permissible unless there is a pressing necessity, or for a clear da'wah (preaching/inviting to Islam) purpose by someone qualified for da'wah, provided that it is highly probable that one will remain safe from falling into the widespread abominations there. This is based on the hadith (definition): "I am free of any Muslim who resides among the polytheists," which was narrated by Al-Tirmidhi, Abu Dawud, and Ibn Majah.