The 2028 RNC primaries are shaping up to be a royal rumble

[Prairie Gates]

6. Hillary lost

For the record, and I assume this is why you didn't name them, the six who have served as Secretary of State were

Thomas Jefferson
James Madison
James Monroe
John Quincy Adams
Martin Van Buren (Shout out to the Van Buren Boys at Lorenzo's heyooo! Eight fingers, son.)
James Buchanan

I'll reiterate, with a qualifier that takes your evidence into account: Cabinet positions don't seem a good route to the modern Presidency. I'm sure you're more an expert than I am, but the only exception I can think of is George HW Bush, who served as Ambassador the the UN under Nixon, and subsequently ran a competitive primary against Reagan, and became his Vice President, and served in that role for eight years before being elected.