I'm looking for a gender neutral word for a person that you are in a romantic relationship with, but not married to. Similar to "partner" in English.
I also want it to be fairly neutral regarding age and to work in formal settings.
Which word can I use?
恋人 perfectly fits your need, its gender and age neutral, and can be used in formal settings.
情人 somehow fits your need, but is not as good, because it could also mean an extramarital lover, which may cause misunderstanding.
爱人 is also gender neutral, but usually refers to partner in marriage.
This is another suggestion:
另一半 (literally, another half)
Example:
男人都喜歡保護另一半。
Men like to protect their partner (another half).
The term 对象 "partner" is also an option: gender neutral, age neutral, perfectly acceptable in formal settings.
It has also other meanings ("target", "object" of something) but the meaning "partner" is quite common as well.
