There are many ways to understand/implement category aliases. To expand the list of solutions investigated in T228065: Investigation: Category link parameters to support aliases and T227877: Investigation: Category redirects as aliases this is about a "real", first-class alias system where:

• there is always a "main category" that can have alias names ( e.g. Physiker => Physikerin / Kartoffel => Erdapfel )
• aliases are defined either on the "main category" page or coming from an external source ( e.g. Wikidata )
• aliases to a category are transparently visible on the related category pages
• aliases can be used everywhere in the wikitext like [[Category:Alias]]
• alias categories will be displayed with the alias used in the wikitext
• alias categories might directly link to the "main category"
• alias categories can be used in URLs but always "hard hard" redirect to the "main category" page
• there are no visible / editable "alias category pages"
• the "main category" page always lists all articles, also from the aliases

• alias categories can be searched for and you'll always find all articles ( at least for MVP, we might make that transparent somehow )