You need to download a file in order to see it somewhere else besides the browser… how can the PDF program know what file to open if you haven’t downloaded any file? that’s your first mistake about understand the issue you are complaining about.
It is clear what that setting to ‘open’ and ‘download’ means and why Chromium team made it the way they made it; either downloads the PDF file or it will open it in the browser 99% of the times, if not it will download it. I don’t get how that is not self explanatory.
But anyway, the File Association is something about the Operating System anyway, so if you want to open your PDF always inside your preferred software, then you HAVE to make sure Brave is not the default PDF application. Second, you have the change the PDF setting to always download the PDF.
And then in theory, you have to download any PDF file, then right click in the PDF file and set it to OPEN WITH SYSTEM VIEWER
which will automatically open it once you download a PDF file, and that will apply to any future PDF file you download in your preferred software, Brave or any other PDF reader.
So, if the Browser already gives you the option to download every PDF file, and that’s what you want in order to open it automatically inside your preferred PDF reader, then use it, you have to set it up, because people’s needs are different, some people might want to download every pdf but don’t open it automatically, or do what you want, download a PDF and open it in an external program.
So while the “open with system viewer” is the only thing you can complain about about where it is placed, you could have easily asked how it is achieved, my post would be the same, and your post wouldn’t have been 3 paragraphs of “I don’t like it”.
But the problem you don’t seem to understand is how external PDF readers can’t just read a file that doesn’t exist in the disk in a normal location, so yes, you have to download it in order to use it outside the Browser, external PDF readers can’t and won’t read Browser’s data the way the PDF viewer does, where in Chromium/Brave, the PDF viewer is an extension.