Verb+est 的問題

The word (close) here is not a verb.

Peter closed the door. (Closed is a verb).

Mary is close to me. (Close is not a verb. It is an adjective.)

We would not add est to a verb. We would add est to an adjective.
For example:
Peter is tall.
John is taller than Peter.
David is the tallest boy among them.

I don't think "closest" is a verb. Indeed, it is an adjective. I think this sentence is a relative phrase.

close the door - verb in this sentence -opposite to open

the closest to the door = adjective not verb = near or nearest to the door