PDFs opening in Chromium despite Acrobat being set as default

So the solution to this was to disable HP Sure Click (which was what the small blue icon discussed above was). Sure Click was rerouting any unverified pdfs from email or the internet to Chromium. You can either disable this protection on a case-by-case basis by right-clicking the file and then selecting 'Remove protection', or you can simply disable the entire HP Sure Click app.

As already stated on the comments and previous answers, Chromium is a web browser and not a virus.

One more thing you can try is to set Acrobat as default reader via its settings. Open Acrobat, on the menu, click Edit > Preferences. Click on General. On the right pane, go to the bottom, click on "Select as Default PDFs Handler". Follow the instructions.

At least for now, also check "Tell me if Adobe Acrobat Reader is not my default PDF application" for Acrobat to warn when it is not the default app to open PDF files.

Chromium is a web browser that is a basis for Chrome and others. Here's a Wikipedia article on Chromium. It's safe.

I suppose Chromium somehow hijacked Adobe Reader's PDF handler and now when a file gets associated to Adobe Reader, Chromium's executable is used to open it.

Try to uninstall Adobe Reader and install it again. Hopefully this will recreate file associations and handlers.

Chromium is an open source webbrowser.
The main part of it (the "engine") is also used by Google Chrome, Opera and the latest version of Microsoft Edge. (And there are a bunch of Linux browsers as well that are based on Chromium.
So Chromium is not a virus.

What has happened is, that at some point, someone set Chromium as the default PDF handler on your computer. (All modern browsers, including the Chromium based ones, can be used as PDF reader too.) You may have done this yourself or whatever program that installed Chromium did that for you.

To switch it back to Adobe you need to tell Windows that you want to use Adobe. This is NOT a setting you can change in Chromium or in Adobe. It is a Windows setting.

Open the Settings, find the "Default Apps by File Type" section.
On the left-hand side look for .pdf in the list. It should show Chromium on the right. Click on Chromium to change that to Adobe (or any other program that can handle PDF, you will be shown a list).