I've been working with databases for a while now and I know privacy concerns well. The good news is you can do this locally, without sending anything to the cloud. The most straightforward way is to use a tool like Ollama or LM Studio, which let you run language models on your computer. Then you upload your PDFs to a tool that creates an "index" of the documents (RAG - Retrieval Augmented Generation). Basically the system reads your files, extracts the important information, and when someone asks a question, it searches your data and answers based on what it finds.
If you want something simpler, there are platforms that run locally, like Hugging Face's Transformers or even local ChatGPT (using ollama). You need a decent computer with some RAM and maybe a good graphics card if you want speed, but it works. There are also open-source options like PrivateGPT or LocalAI that do exactly this - they process PDF documents and create a chatbot without anything leaving your home.
The big challenge is that it requires some technical knowledge. But if you're comfortable with command lines and basic Python, there are tons of tutorials. If you'd rather have a graphical interface, LM Studio is pretty accessible. Privacy is guaranteed because everything stays on your hardware.