How to create custom search filter for entity list
You are using an entity list builder? There is no standard support for filters/sort, if you want to implement something you have to do it yourself.

All content lists that use filters like admin/people and admin/content are views, expose your entity type to views if it is a content entity type.

One special case is admin/structure/views, which is a config entity list builder that has support for filters. But that's actually a client-side implementation done with javascript.