Recently I was working with this ISV who was developing an Outlook Web addin. They use SupportsPinning in Outlook Web addin and noticed that its not working as expected. When I debugged further I noticed that they’re using older Outlook 2016 build. So when I looked at the documentation, I can confirm that the support for pinnable taskpanes is currently available to specific versions of Outlook on Windows. So, “Pinnable task panes are currently available to Office 365 subscribers on Outlook 2016 or later for Windows (build 7668.2000 or later for users in the Current or Office Insider Channels, build 7900.xxxx or later for users in Deferred channels), Outlook 2016 or later for Mac (version 16.13.503 or later), and Outlook Online.”. Please make sure you have the Outlook builds mentioned above or I would recommend you to get the latest one and see it helps you moving forward.
Still if it doesn't work then I recommend you to check the sample addin that we provided or the sample code that we published in the above said documentation. This sample Command Demo add-in uses the commands model for Outlook add-ins to add buttons to the ribbon.
Hope this helps.