Doesn't help you in the slightest, but when I look at the default browser (set to Firefox) and click on the icon, I see a display headed Choose an application.
For me, the list includes:
Microsoft Edge - Blue/green snailshell-like "e" on a brownish background. Google Chrome Internet Explorer Microsoft Edge - White "e" on a blue background.
Look for an app in the Microsoft store.
This PC was built/installed as a new Windows 10 installation just under a year ago and has been kept pretty much up to date throughout - Firefox and Windows.
The programs all get "migrated" during one phase of the upgrade.
I presume this rebuilds parts of the registry, without them being carried over directly.
Some programs can be "removed" by the migration process, so anything on the blacklist would be cut. An example on a Win7-Win10 Upgrade, would be removal of Windows Virtual PC, a Microsoft program. It's used for WinXP Mode, and WinXP Mode would be removed by an Upgrade.
The process is likely to "refresh" Program Files. I thought the Windows.old had a Program Files and a few other things like it, contained inside, and used if a revert needs to be done after the Upgrade finishes.
And doing a revert is not perfect - you don't get back your Windows 7 exactly and precisely as you left it. The odd setting gets changed.
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I've been trying to find a reference for how program registration works. It seems the application manifest (could be a file in the .msi for example), you can put mention of http or https handling in there. And that would be a portion of registering a browser. But I can't find details of whether TrustedInstaller does this, msiexec does it, and also which step drives it. There are claims that if you re-register http or https handlers, that the system will then make your "browser" appear in the Default Apps section. But this seems a hopelessly manual way of fixing things.
Reinstalling won't fix it, unless whatever step is missing magically gets done the second time. And that doesn't seem likely. First you have to fix whatever is the root cause, and *then* reinstalling stands a chance.
This is a pretty old reference. To follow a similar path, you'd have to figure out where the log it produces is put.
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There does seem to be a way to turn on msiexec logging. Even though anything important should be throwing an error onto the screen during an install.
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And while you could run Sysinternals Process Monitor during a Firefox installation attempt, then look to see if anything is updating those critical registry settings, that's probably more trouble than its worth. It's probably better to get msiexec logging working instead.
And the Firefox installation is available as an MSI file, if you want to make sure an MSI is used for the process.
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File Firefox Setup 82.0.3.exe 54M 09-Nov-2020 10:08 File Firefox Setup 82.0.3.msi 55M 09-Nov-2020 10:08 Right-clicking it after download should say "Install"
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