"about me" versus "about I" [closed]

Consider the following sentence:

The details in the first section are the most important ones about me.

The sentence seems completely natural, and yet, by analysis it appears that "the most important ones about me" is a subject, not an object, by which observation, to follow the standard grammar, "me" must be changed to "I".

The result is as follows:

The details in the first section are the most important ones about I

This sentence seems unnatural. Is it correct, according to standard grammar?

It is the word "about" that determines whether to use "me" in this case.

This book is about me
This book is about you
This book is about her
This book is about us
This book is about you
This book is about them

similarly with "for"

This book is for me
This book is for you
This book is for her
This book is for us
This book is for you
This book is for them

Other prepositions require the use of "me", e.g.

Give it to me.
Stand by me.
Stay with me.

No, your second sentence is not correct.

You are correct that the verb be (here appearing as "are") does not take an object, and that "the most important ones about me" is effectively a subject. (Actually it's a subject complement.)

But "about me" qualifies the head noun most important ones which is in the subjective case. In English, prepositions take the objective case, and it's about me, not about I.

That is, within a noun phrase, even one which is a subject complement, it's perfectly possible to have something appear in the objective case where the grammar [of a preposition, say] requires it.

While I can see the argument for "the most important ones about me" being a "subject" (if the full sentence were "The person in the first section is ___", you could make a case for either "I" or "me"), the question is what role "me" has within "the most important ones about me".

And within that, "me" is not a subject, but rather the object of the preposition.

It serves to describe the "the ones" ("the most important ones which are about me"), and in that sense can be thought of as the "object" where the "subject" would be "the most important ones".