https://www.senate.gov/about/powers-procedures/treaties.htm#:~:text=The%20United%20States%20Constitution%20provides,become%20part%20of%20international%20law.

Instead, the Secretary of State, Antony Blinken, does.

https://www.state.gov/treaty-procedures/

With review from his department’s Legal Advisor, Richard C. Visek.

https://www.state.gov/bureaus-offices/secretary-of-state/office-of-the-legal-adviser/

Richard Visek

https://www.c-span.org/video/?518295-1/deputy-secretary-state-testifies-war-powers

https://www.state.gov/biographies/richard-c-visek/#:~:text=20%2C%202021%20%2D%20Present-,Richard%20C.,Department's%20Designated%20Agency%20Ethics%20Official.

Why can the Department of State sign treaties instead of the President?

Because according to the Senate, International Law has replaced the Constitution.

https://www.senate.gov/about/powers-procedures/treaties.htm#:~:text=The%20United%20States%20Constitution%20provides,become%20part%20of%20international%20law.