Correct. In order to serve, one must meet the requirements of the Constitution.
But you have not been talking about serving. You’ve been talking about “running for President”, which is not a concept with any Constitutional restrictions, except as provided by the laws of fifty states.
You are putting too fine a point on this, imo.
It is highly doubtful if not a certainty that any State would even allow, since it is at the discretion of the State, a candidate to even appear on the ballot if they were prohibited from serving in the office for which they are running.