Is it a problem if we don’t live together but are legally married? 

It could raise a red flag. USCIS expects married couples to live together, so living apart may lead to extra questions about whether your marriage is real.

The longer you're apart, the more suspicious USCIS may become especially with little communication or evidence of your relationship.

If you're applying to remove conditions (Form I-751), living apart can make that harder unless you file with a waiver or explain the situation.

You'll need strong proof your relationship is genuine like photos, messages, travel records, and joint finances.