I'm not finding any information on windows update KB5991567. Is this the correct update?
Flash Player reached end-of-life at the end of 2020 and most browser vendors have removed support for Flash Player.
With that said, Adobe, and browser vendors announced in July 2017 that Flash Player would reach end of life at the end of 2020. This gave content providers (in this case Logitech) over 3 years to prepare and remove Flash Player support from their products. Logitech is the one that needs to fix this in their product to use some other technology besides Flash.
Logitech's comment "However as per checking Microsoft has released a Windows update that removes Adobe's Flash Player before it reaches end of support on December 31, 2020." is confusing. I wonder if they are referring to KB4577586, which while released last year, was optional, not required, and users had to actively look for it and run it to remove the bundled Flash Player. It was only within the last month or so that Microsoft started including this in their update (see https://www.bleepingcomputer.com/news/microsoft/microsoft-force-installs-windows-10-update-to-remove-flash-player/)
For reference:
https://theblog.adobe.com/adobe-flash-update/
https://www.adobe.com/products/flashplayer/end-of-life.html
Browser support information:
Apple Safari - Flash Player support removed in Safari 14, released Sept 16, 2020
Google Chrome - Flash Player support removed in Chrome 88, released Jan 19, 2021
Firefox - Flash Player support removed in Firefox 85, released on Jan 26, 2021.
Firefox ESR 78 will support Flash Player for the time being, assuming the Flash Player NPAPI plugin is already installed on the system as it’s no longer available for download.
Microsoft Edge - Flash Player support removed in Edge 88, released Jan 15, 2021
Legacy Edge & IE: KB4577586: Update for the removal of Adobe Flash Player: October 27, 2020
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