GNOME extension is incompatible

I used Ubuntu 20.04 for a few months. This is the third I'm using Ubuntu 21.10 and I cannot install this GNOME extension: Emoji Selector

How can I fix this?

You are facing the major drawback of using Gnome Shell extensions from the Gnome Website. Gnome Shell unfortunately breaks extensions frequently. The author then needs to adapt the extension to mach the newer Gnome Shell version. If that does not happen, the user has a problem. There is nothing you can do except signalling the issue, and hoping the author will pick up, apart from going into coding yourself.

• You may prefer to install extensions from Ubuntu software. These are packed and tested to work with your desktop. This is a selection of extensions that is rather stable, although even there, there is no guarantee that an extension will be available in a next Ubuntu version.
• You may prefer to select a Long Term Release Ubuntu version. Such system is supported for a longer time, so you are less likely to have to adapt your workflow because some components you rely on stop working.
• Unsupported: you can force the extension to be loaded in your current version of Gnome Shell by changing the version number in the metadata.json file of the extension with a text editor.

There are other emoji tools which are independent of GNOME shell. For instance: If you open Ubuntu Software and search for emoji picker you'll find one such tool which you may want to check out.