The cheat way would to use one of the closing templates. At enWS we normally template such formatting so we would not notice it particularly ... the {{nnnn block/s}} and {{nnnn block/e}} templates where the "/e" version is usually a </div> template, or an open/close {{nnnn block|}} where the }} is all that sits in the footer.

So create {{div end}} with a hard return and </div> should sort out the code.

I do see the following discussion that may be related
https://en.wikisource.org/wiki/Wikisource:Scriptorium/Archives/2016-09#Which_tags_are_excluded_in_a_page_footer.3F

In T155362#2942471, @Billinghurst wrote:

So create {{div end}} with a hard return and </div> should sort out the code.

This is a bit different case (the formatting being removed is intended to be used in Page namespace only, unlike your example), but the solution may be indeed similar (creation of wrapping templates).
I am just running pywikibot touch over Page ns in plwikisource, so I expect to locate all uses of </div> found to be controversial.

However the main problem I see here is that the potentially breaking changes and a solution are not loudly announced over wikisources. Is Tech News wrong way for it?

Another problem I noticed if the presence of (illy formatted) <div class="pagetext"> in the header of this page:
https://pl.wikisource.org/wiki/Strona:PL_Miko%C5%82aja_Kopernika_Toru%C5%84czyka_O_obrotach_cia%C5%82_niebieskich_ksi%C4%85g_sze%C5%9B%C4%87.djvu/014
even after cleaning (which I expected to remove this). I doubt anybody did interfere into header/footer content in this case: anything there was likely automatically created. @Tpt : should I open another bug for this case?

For ease of testing, here's a currently affected page on English Wikisource: https://en.wikisource.org/w/index.php?title=Page:Our_Neighbor-Mexico.djvu/12&oldid=5679841

Opening it for editing and clicking "Show changes" shows a </div> in the footer being removed:

When viewing raw wikitext: https://en.wikisource.org/w/index.php?title=Page:Our_Neighbor-Mexico.djvu/12&oldid=5679841&action=raw, there is a <noinclude></div></noinclude> at the end, but this tag is not shown when opening the edit form. It matches the opening tag <noinclude>…<div {{ts|width:500px;|ma|aj|lh13}}></noinclude>.

(I found this page with: https://en.wikisource.org/w/index.php?search=insource%3A%2F%5C<noinclude%5C>%5C<%5C%2Fdiv%5C>%5C<%5C%2Fnoinclude%5C>%2F+-insource%3Apagetext&profile=all)

Presumably, a closing </div> should only be removed when we also removed an opening <div class="pagetext"> (which is required for conversion from the old format, and invisible in diffs).

Change 439652 had a related patch set uploaded (by Bartosz Dziewoński; owner: Bartosz Dziewoński):
[mediawiki/extensions/ProofreadPage@master] PageContentHandler: Do not remove unmatched </div> when unserializing wikitext content

https://gerrit.wikimedia.org/r/439652

Change 439652 merged by jenkins-bot:
[mediawiki/extensions/ProofreadPage@master] PageContentHandler: Do not remove unmatched </div> when unserializing wikitext content

https://gerrit.wikimedia.org/r/439652