Algolia is definately a nice solution.
https://www.algolia.com/doc/guides/search/filtering-faceting/
I found it that instead of inventing a wheel it is good sometimes to use something ready and tested. Take for instance a invoicing - I always thought that I will have my own better system, but there such a huge amount of great saas these days with with API that there is simply no point spending time and money to develop your own invoicing anymore.
I would use the same principle here.