The problem is that the Kindle expects cover thumbnails (for Cover View) to be downloaded from Amazon's servers, based on the book's ASIN identifier (mobipocket's exth 113 metadata header).
For PDOCs the Kindle will extract a cover directly from the book itself, but
only for PDOCs.
calibre will circumvent this issue by sideloading a cover thumbnail for books with a cdetype of EBOK, when using Send-to-Device. This copies the generated thumbnail image to where the Kindle expects it, inside [userstore]/system/thumbnails/
Needless to say, calibre cannot do that from the experimental browser.

No, there is no workaround, you must use the USB connection.
(Alternatively, you could sideload all your books as PDOCs, see the relevant MOBI Output option in calibre's conversion preferences. Then you get the ugly "Personal" banner and the book is sorted under Personal Documents.)