Elastic search is free if you self host it. You are only charged if you want to rely on their infrastructure or some advanced features. From what you're saying, sounds like an inverted index is more than enough for your use case which is a free feature.

I have used elasticsearch for simple use cases via docker. https://hub.docker.com/_/elasticsearch

Just spin up the container and index the extracted text data. Then you can run queries against it.

For Papermerge I am not sure. I had heard about it some time back and it looks like the project is abandoned or updated infrequently