What is the definition of "religion" linguistically and Islamically, and are democracy and socialism considered religions?

The word "deen" (religion/way of life) is mentioned in the Arabic language with several meanings, including: the way/method, the recompense/requital, the conduct of the king, politics/governance, and obedience and submission. As for its meaning in Islamic law and the Holy Quran, the meaning of "deen" does not depart from its linguistic meanings. Some of these include: Allah's حكم (judgment/ruling) and obedience to Him, the system and law of the ruler, and the Day of Recompense and Accountability. Therefore, whoever takes democracy, socialism, or any system other than Islam as an ideology, a system, or an authority, has embraced a "deen" (way of life/religion) other than Islam.