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I have two scholarly books self-published in the field of physics. However, some parts of my books have previously been published in peer-reviewed journals and the editors of my books have academic positions.

If I can succeed in republishing more parts of my self-published books in peer-reviewed journals

  • does this implicitly indicate to the reader/buyer that the books have somehow been peer-reviewed?
  • Do these in any ways improve the significance of my self-published books, considering the fact that excessive self-citation is a red flag to many academics?
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    You almost certainly cannot publish in any sense, either self or otherwise, work that has previously been published in a journal. You would need the journal's permission for that, and I guess they haven't given it, because they usually only do that for collected works or other reasons. Conversely, you cannot submit to a journal work that has previously been published as a book. So none of this makes sense.
    – David A. Craven
    Mar 19 at 0:15
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    @DavidA.Craven In the first case, I think it is possible to publish in a book a modified version of the previously published articles or the articles which have been published as open-access distributed under the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the second case, since the author retains the copyright when they self-published a book, I think there is not any significant issue with republishing (at least a modified version) in a journal.
    – Mohammad Javanshiry
    Mar 19 at 0:30
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    If you are CC BY then sure, you can do what you want. If you publish your work anywhere, and then submit it a journal afterwards, you will normally violate the journal's ToS, which require all work to have not been published before. Maybe you can find a journal that publishes already published stuff.
    – David A. Craven
    Mar 19 at 0:37
  • Books in physics are usually not peer-reviewed: it would simply take forever to review this. Books are “evaluated” in the sense that the skeleton of books (possibly including selected sections or chapters) are often distributed to specialists for comments, but that’s not peer-review.
    – ZeroTheHero
    Mar 19 at 3:07

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Almost surely not

Because the material has already been published before.

Reprint volumes (i.e., collections of works by some famous author, e.g. this) are generally not very valuable, and also not very profitable, which is why publishers don't often do it unless the person whose work is being featured is very notable. If you are self-publishing, then chances are you are not one of these very notable people, and a collection of your works is not likely to be a "valuable scholarly book".

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  • Reprint volumes can have value in that they collect in a single place a number of worthwhile articles on a specific topic. Certainly the collected papers of -say - Hans Bethe or Julian Schwinger, or a reprint volume of early seminal papers on coherent states, are of immense value. However, things are not the same in the reverse direction : slicing up a book in individual papers after the fact risks shining a dark light on those sections not published while sections that get published merely meet expectations by being publishable.
    – ZeroTheHero
    Mar 20 at 3:32
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In the context of your 'question', beware of the path.

Nonetheless, regarding the content, the following comes through:

... two scholarly books self-published ...

Self-published or otherwise, there are two fundamentals: what is scholarly and what are scholarly books.

Irrespective of many opinions, a fundamental remains that scholarly pertains to academic and research. The elements, amongst others, are validity, reliability, rigour, ethics.
These are what reviews ought to safeguard.

Scholarly books ought to have these at their core, however in different shades unlike articles.
Scholarly books can also be books for teaching discipline subjects or can simply be monologue of collections. Are they scholarly, well they are. Do they extend/contribute to knowledge, they might. Would they be scholarly in the context of validity, reliability, rigour, ethics ...; That would comes through like a ... the proof is in the pudding

republishing more parts of my self-published books

I'll say, explicitly so, what you are republishing (as an article) cannot and shouldn't be those parts of your self-published books that were "previously been published in peer-reviewed journals".
If however any of these previously been published in peer-reviewed journals is/are to be republished, the word and the process is not that of 'republishing' but rather of publishing through the manuscript, review, publish process.

does this implicitly indicate to the reader/buyer that the books have somehow been peer-reviewed

First thing first, it is either it's been peer-reviewed or it's not been peer-reviewed. There's no 'somehow' Secondly, it must be pointed out that peer-reviewed referred to the 'object' and not the 'form'. So, if the book and the chapters are not peer-reviewed as a collective entity, then it's not peer-reviewed. It's that simple. It's immaterial if post book chapters are peer-reviewed afterwards, it's immaterial in so far as the 'peer-reviewness' of the book itself is concerned. The post publication actions do not validate the already published book. It is inconsequential and nullity, as would be said in law; regarding the peer-reviewed

Do these in any ways improve the significance of my self-published books...

I'll say emphatically NO
Nonetheless, I'll still say, significance here is subjective. In any case, in the context of your 'content', the focus should shift to

  • are others referring to the books and/or its chapters
  • are the books being embraced
  • are the books being scholarly engaged; whether critique, critic, complement, reconstructive, progressive...
  • are works been derived from the books by others apart from yourself
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