If the pdf files are properly formatted (no compression/all text selectable), you should be able to open a terminal and do (I know it works the other way around, not sure if libreoffice can actually do the reverse but it doesn't hurt to try)

libreoffice --headless --convert-to docx *.pdf

Just know that since docx is a proprietary format by microsoft, the results may be flawed. As a last resort I guess you could run a windows VM and try to convert your files with any big software known to be able to handle such files.

I think it will depend on what exactly is in the PDF. If these are text, you can in a pinch just copy and paste it but I'd expect libreoffice to be able to open it. If these are images, you'll have to use some OCR

PDFs are inherently not designed to be edited, the format lacks a lot of the information necessary for layouts to work correctly and as expected.

That's why you have to open it with LibreOffice Draw, and the mess you see is basically the information that's contained within the PDF. It is just a bunch of random text cells randomly placed over the page. That makes it really difficult to get back an editable version that's sensible. Page wraps and such will never work correctly. Your only chance at recovering it is if you can figure out what software wrote it, and how different constructs might end up when translated to PDF and a lot of heuristics.

I believe they open a bit better in Xournal++ but it still sucks.

Those that do build such tools realize it's all big companies with big budgets that really have a serious need to do this, so they tend to be proprietary and expensive, and still not super great.

I would really beg for the files to be provided in a suitable format for editing.

Have you tried pandoc ?

I use self-hosted STIRLING-PDF.

@Maroon
Vielleicht hilft dir der Link aus der LibreOffice 24.2 Help weiter:

Tabellen mit Filternamen für die Dokumentkonvertierung mittels Befehlszeile.

Short answer: No.