Paperwork seems to fit most of the bill except for one thing: it won’t scroll to where the search hit is (but it will highlight the matching keywords).
Just beware Paperwork won’t just create an index. It’ll organize the PDF its own way in its own work directory.
(full disclosure: I’m its main dev)
I think there is some confusion here.
Paperwork is a desktop application, not a web application. (eh, self-hosting doesn’t necessarily always imply web applications ! :). I for one use Nextcloud and nextcloud-desktop to keep my Paperwork work directories in sync on all my computers.