Manticore does support facet search and it's quite powerful in Manticore:
- docs - https://manual.manticoresearch.com/Searching/Faceted_search#...
- interactive course - https://play.manticoresearch.com/faceting/
Search-as-you-type depends more on the client, not on the backend. However, Manticore provides the autocomplete and fuzzy features (both in beta stage though). More info here https://github.com/manticoresoftware/manticoresearch/issues/...