[Quoth]

I add the cover to Calibre and use it to convert Docx to epub.
Then epub or mobi, azw or whatever.
I edit in LO Writer, saving/editing in odt format. I do an EXTRA save in docx for Calibre, and never open that in LO Writer as Writer will ALWAYS convert on load any non-odt file.

The LO Writer (or earlier years, MS Word) never ever has the cover in it.

I edit covers in The Gimp, in layers, stored native at about x4 the resolution for an ebook. I export various resolutions of jpg and png files for different purposes:
Upload to Amazon / Smashwords etc and thence to Kobo, Apple, B&N, Tolino etc. The uploaded ebook has a lower resolution cover added by Calibre.

Then a different jpg might be used for our blog or other promotional material
A paper version will use 300dpi, 400 dpi or 600dpi depending on process/quality and thus a larger book format needs a larger image as the DPI has to be the same.

The same Epub2 is uploaded to Amazon KDP and Smashwords, but Smashwords also gets a dual mobi (because they can't tell what Kindle their customers have) as well as maybe a .doc for additional formats.
Amazon does their own conversion into all their formats from the epub2, including fully enhanced typeset KFX (there is no reason why a Kindle can't have a FW update so azw renders the same). KFX is really about delivery and DRM.

The goal, usually achieved, is that azw, kfx, epub2 should all look about the same and the same as the view in LO Writer. Old Mobi should have at least serif, sans, mono all in normal, bold, italic, bold-italic, larger headings, correct justification, relatively similar relative offsets to non-body margins, TOC, page breaks and links corresponding to the epub2/azw.

Calibre does a good job, but it needs fed with a docx where the styles and TOC are done correctly.
I auto create the index to level 2 (the headings are all level1 or level2 and EVERYTHING not in the index / TOC is body level), copy to a plain text editor, paste back and format.
I put anchors ONLY at the start of a paragraph (each heading is also a paragraph) and then select each line of the text index and edit link. The anchor is entered just in the URL box, not via document browse, just putting # prefix. The anchors are all lowercase with no punctuation, spaces or accents, typically ch2, ch3 etc. Then Calibre makes the ebook NCX from that correctly formatted user index, which is also inline in the ebook.