In the United States, a claim to ownership of a copyright must be registered with the copyright office before a civil lawsuit can be filed against a violator. (However, the violation could happen before the registration.) By law, the Copyright Office is a department within the Library of Congress. That means it is within the legislative branch of the federal government. Since its function is executive rather than legislative, could that situation be considered unconstitutional?
While the argument you make is straight forward, it is hard to imagine who would ever have standing to challenge the law. Who can legitimately argue that they are harmed in any way by having to register with an agency housed in the legislative branch rather than in the executive branch?
Also, there is a legitimate argument that the Library of Congress should be in the legislative branch as a research tool for Congress, and there is a legitimate argument that the Copyright office should be in the Library of Congress because that is how the Library of Congress gets its comprehensive collection of research resources, which Congress in turns uses to make policy.
The Executive branch does not have a monopoly on implementing U.S. laws and indeed, before the copyright registrar function was placed in the U.S. Congress, it was vested in the judicial branch with the clerks of the U.S. District courts, and not in the executive branch.
Furthermore, the agency's director is appointed by the Librarian of Congress, who in turn is appointed by the President with the consent of the Senate despite its location within Congress on the organizational chart of the U.S. Government, so it does not violate the Appointments Clause of Article II, Section 2, Clause 2 of the United States Constitution. In substance, the Copyright Registrar is in the direct chain of command from the President in terms of appointment authority, despite being located in the legislative branch for purposes of day to day management of the Library of Congress and budget categorization.
What do you mean by an "executive" function? If you simply mean doing things rather than creating laws, that can't be right. For example, the Congress and the judiciary both have police.