A shared password should not become a test of affection.

Access to a phone or an account is a practical matter that easily gets recruited into proving something. Once handing it over becomes evidence of love, refusing becomes evidence of guilt, and there is no answer that settles anything. Trust cannot be demonstrated this way; the demonstration only postpones the underlying question, which is usually about reassurance rather than security.

If this is live between you, try naming the worry directly instead of the arrangement. Ask what would actually help, and say what you are comfortable with.