I have software (goddinpotty) I use to publish a personal wiki-like site, and I’d be happy to help you use it for yours if you like (I write the content in Logseq which is similar to Obsidian). One thing it does is let you tag particular pages or chunks of a page as #Private so they don’t get published.
I guess it is pretty similar in functionality to Quartz, which might be easier for you to use, but let me know if interested.