I really hope this is a *dumb user error* because that'll be easy to fix.
I have this happen when updating Edge Dev, then eventually after changing a million things it comes good. If I go to *any web page* and try to download a file (e.g. https://www.co.shasta.ca.us/docs/libraries/resource-management-docs/ehd-docs/Pool_Chemistry_Fact_She... then right-click, save as) the Finder dialog comes up, you navigate to wherever, rename if you like, click the button and the dialog disappears. The 'download file progress' icon never appears, the file doesn't download, etc, etc. If you try to exit Edge (or the Update installer tries to restart it to do the update), Edge warns you that 'There are downloads in progress, do you really want to...', etc.
Hi, Edge should open that link which is PDF automatically inside browser unless you changed the way it handles PDFs. anyway, please try resetting Edge settings back to defaults: edge://settings/reset disable your extensions: edge://extensions/ reset custom flags, if any: edge://flags/