Typesense is an open source alternative.

If you cannot self-host it, there is a paid cloud option. It differs from Algolia in that they do not charge by records or search operations. Instead, you get a dedicated cluster and you can throw as much data and traffic at it as it can handle.

https://github.com/typesense/typesense

https://cloud.typesense.org/pricing

Look for a solution that doesn't solve everything Algolia does. Hard to say what that is exactly for your company as you don't explain what "basic search" is.