I have had the same problem consistently for the last two years as well: PDFs loaded in the browser are usually not recognized by the extension as PDFs (they are recognized as web pages), and, even when the extension does correctly recognize the URL as a PDF, clicking the item does not result in the PDF being stored in Zotero.
When I first go to this link, the extension shows the webpage icon, not the PDF icon, and, when I click the extension's webpage icon, nothing happens. Normally a forced refresh will turn the extension's icon into a PDF icon, but usually, when you click that icon, still nothing happens. A third refresh *sometimes* allows me to click and save. I usually just end up needing to save the file locally and then switch to the Zotero app to store it directly from the local disk. I'd love to be able to simply click the icon and see Zotero consistently recognize the PDF as a PDF and store it for me.
The behavior seems truly random: sometimes the exact same page will load as a PDF and sometimes as a web page, and sometimes the PDF will store to Zotero when you click the icon and sometimes it won't. For what it's worth, I have seen this behavior consistently on multiple machines and operating systems and in Chrome as well as the Chromium version of Edge.
(I debated on whether to open a new thread, but I thought it would be best to respond to this one, as it seems that I am having the same core problem as the OP.)
(When in doubt, it's always better to start a new thread. There's some confusion about how things are supposed to work in the other thread that makes it more complicated to continue there. You can always link to another thread you think might be relevant.)
Have you tried disabling any other extensions you're running?
If you can reproduce this reliably with other extensions disabled, we'd want to see a Debug ID from the connector for navigating to a PDF from another page and not get the PDF icon.
Upgrade Storage
Take, for instance, this file: https://www.opalco.com/wp-content/uploads/2014/10/Reading-Sample-Size1.pdf
When I first go to this link, the extension shows the webpage icon, not the PDF icon, and, when I click the extension's webpage icon, nothing happens. Normally a forced refresh will turn the extension's icon into a PDF icon, but usually, when you click that icon, still nothing happens. A third refresh *sometimes* allows me to click and save. I usually just end up needing to save the file locally and then switch to the Zotero app to store it directly from the local disk. I'd love to be able to simply click the icon and see Zotero consistently recognize the PDF as a PDF and store it for me.
The behavior seems truly random: sometimes the exact same page will load as a PDF and sometimes as a web page, and sometimes the PDF will store to Zotero when you click the icon and sometimes it won't. For what it's worth, I have seen this behavior consistently on multiple machines and operating systems and in Chrome as well as the Chromium version of Edge.
(I debated on whether to open a new thread, but I thought it would be best to respond to this one, as it seems that I am having the same core problem as the OP.)
Have you tried disabling any other extensions you're running?
If you can reproduce this reliably with other extensions disabled, we'd want to see a Debug ID from the connector for navigating to a PDF from another page and not get the PDF icon.