Yes, and it's scoped by either domain or (rarely used) types from the schema.org ontology. You can't use it to just search the web.

You can use it to search the web; you don't get the exact same experience as the old API.

https://support.google.com/customsearch/answer/2631040?hl=en

Neat. Now it's just a matter of dealing with the absurdly low free usage limit and absurdly expensive paid tier.

Then it's just a market forces question. Use a provider of search services which matches your budgetary/usage requirements.