Convert PDF schematic to any form of schematic files like .sch
This is not an unreasonable ask. After all, it's possible to import PDFs into Word and edit them, so why not schematics too?
There's some issues.

The PDF itself won't carry all the needed information to make a schematic.

Although PDFs (being descended from Postscript) have embedded graphic information, the object data won't carry the defined relationships between elements: how they group, how they connect. Further, any non-visible component and connection attributes that were in the schematic will be lost in translation to PDF.

You're at the mercy of how the schematic tool generated the PDF.

If you're lucky you have objects which you can find. If you're not, you could just have a raw compressed bitmap for which PDF is merely a container.
That said, it's theoretically possible to infer those relationships by screen-scraping the printed pages and identifying the elements and connections. It would be an interesting project as a thesis, and possible product were someone to undertake it. This would be a good use of AI for example.