You are exactly correct. A lot of Americans think of the President as the sole arbiter of government authority, despite the fact that they are just the head of one of three branches of government. As head of the Executive, they have a ton of agencies and advisors who report to them.

This is true, but the president (or presidental candidate) is also the face of their backing party, and that matters a lot. We've seen other people try it, but Trump is the only one who can really whip up the MAGA frenzy, which is why conservatives have painted themselves into a corner with him. Likewise, Biden represents what democrats find frustrating about the party: out of touch geriatrics who promise nothing but more of the same.

So yeah, while the president isn't doing most of the work directly, they set the tone, and they have a lot of influence over (or direct power to appoint) people who run major things.