SPFx Field Customizers only provides modified views for fields within a list and those are client-side components that run inside the context of a SharePoint page.
So, as per my understanding filters will not work on the field as you mentioned as it does not store/modify column value in list (at backend).
Looks like your yeoman package is outdated. Try the following command to get the latest version:
npm install email@example.com -g
As of today, yeoman v4 is not compatible with the SPFx generator. this is why we install v3.