Can you point me to the as-you-type full-text search on Mac for a directory transitively containing 20,000 pdfs?

Sure, Spotlight has been around for at least a decade; it's the little magnifying glass at the right end of the main menubar. It definitely indexes PDFs with a text layer as well as other document formats; I've been running them through OCR for ages and have 28,000 in my records. You can also install extensions for other formats.

It indexes your whole disk; if there's a limit as to how many files it will index, I've yet to reach it. I checked Apple's developer documentation, and they don't mention one.

I use Apple’s built-in Spotlight search to search in Markdown files and PDF documents, albeit I do not have 20,000 of them. Would it be a problem for Spotlight to index 20,000 PDF documents?

Pro's for grep/silversearcher/etc.: quite fast, quite efficient, redirect-able to other tools, maybe a little sqlite here, maybe a bit of xml/svg there and most important of all: private, under my control...

mdimporter: yeah, sure, just no .. mmkay?