Chromium (or Chrome) and hypothes.is
With Chromium you can search for titles in open tabs. I opened 50 tabs (local PDF) - 125 MB in one shot. I added more tabs by dragging and dropping on the window.
hypothes.is require an account. This free and open source project is a system which allows annotation of web pages and PDF. You can run it on local files if you check an option. First you have to create a private group if you want to keep your notes private (you have to select the group in MY GROUPS - than it should keep this as default). The annotations will be on the cloud (with the advantages and the inconveniences). There is a search page for annotations and an API. You can also take notes.
I think Okular save the highlights in the PDF. Don't know if you can search in all annotations. Chromium use more CPU than Okular. I rendered all PDF in Chromium, maybe you could lazy load them.
I made this Bookmarklet to load a PDF with hypothes.is menu in case the original button doesn't work.
bjfhmglciegochdpefhhlphglcehbmek is the identification in the store.
You can annotate, take a note or highlight.
In my opinion, the search in tabs in Firefox is better than in Chromium. You can search
bio co (for Computational biology) and it will show you the corresponding tab. In Chromium you can add an extension for a better search than the default. Firefox doesn't allow extensions to run on PDF. You can bookmark a PDF page (it add .pdf#page=7 at the end of the path), however it will not be associated with the original. You can use use the arrows (left, right, up and down) or j and k.
For searching in all open tabs titles (PDF and HTML) in Firefox, you only have to type
% . Percent sign followed by a space in the address bar.