The president has absolute authority to access to all secrets within the executive branch, and has absolute declassification authority, both statutorily and presumptively constitutionally as a result of a) being the president, b) being able to nominate his cabinet, c) being able to issue executive orders to his executive branch officers and acting officers.

The president therefore has the authority to access every last secret and every last system within the executive branch. No statute can limit this power. The president also has the authority to delegate (to some extent; only the president can issue EOs, but presumably his officers can recommend EOs to him) these powers to his or her officers.

The titular of the U.S. Digital Service (DOGE) is statutorily not subject to Senate confirmation, though considering how Trump's controversial nominees have sailed through Senate confirmation it's easy to suppose that Musk would also likely be confirmed to head the USDS were it an appointment subject to Senate confirmation. Since the president can appoint someone like Elon Musk to head the USDS, and since the president can delegate his clearance and declassification authority to someone like Elon Musk, his doing so does very much "pass [the] sniff test".