That article does not seem to mention generic troubleshooting steps — if you check Troubleshoot and diagnose Firefox problems there's 3.) trying restarting in Safe Mode, and 6.) trying a fresh disposable profile — to see if the woes persist across isolated sessions and profiles.

I tried Troubleshoot (or Safe) mode. I tried a new profile. None of these changed anything. The article I mentioned suggested these. In summary, I did the following.

1. Restart your computer 2. Clear your cookies and cache 3. Restart Firefox in Troubleshoot Mode 4. Reinstall Firefox 5. Refresh Firefox 6. Create a new Firefox profile

Plus, I used "about:config" and looked for the "browser.download" options, but then realized that I didn't really know what they were supposed to be, and so didn't change any of those. The page that I found that suggested the following 5 config settings:

browser.download.dir browser.download.downloadDir browser.download.folderList browser.download.lastDir browser.download.useDownloadDir

but I only have browser.download.folderList (1) and browser.download.useDownloadDir (true).

This might very well be a candidate for filing a bug, if a fresh profile exhibits the same:/

Couple of obnoxious questions: Is this a recent change? Do you recall if/when this worked as expected? Does your installation come from Flatpak, some RPM repo, or a Mozilla binary? Would you be willing to try the official Mozilla RPM repo for the most "vanilla" experience? If you feel it's a recent change, would you be able to run mozregression to see if there's a good/bad version boundary at some revision?

Sorry if this is stupid question: Do arbitrary downloads work, like… just clicking https://file-examples.com/wp-content/storage/2017/10/file_example_ODP_200kB.odp — or clicking the image in https://www.w3schools.com/tags/tryit.asp?filename=tryhtml5_a_download that should "just" download, somewhere, and trigger the previously hidden toolbar icon with it.

Or this only affects the "Save as…" elements from contextual menu?

An excellent question! Those two links download just fine. And I now have a download button in my toolbar. (Clicking on it, it shows a button for "Hide Button When Empty", which would explain why it was missing, I guess.)

This seems just to be a problem with "Save Image as", and maybe the fact that the "Browse" button doesn't work in Settings to set the Download directory.

Also, I have google-chrome on my system, but normally don't use it unless Firefox seems to not work. But if I bring it up, it has the same behavior. -- Save image as does nothing, And if I go to Settings, Downloads, the "Location" is given as ".../Downloads" but the Change button next to it does nothing. So I suspect that the about:config code is all the same for Firefox and Chrome, and this is where the problem is. Possibly something like the browser.download.dir entry has disappeared for some reason, and the code to access it gets back a NULL and then just punts when I ask it to save a file. Same for the Browse button -- it goes to get the current value, gets a NULL, and just returns. But that's just a guess.