I've always done dev sites in my dev browser, so good to hear from this:
https://polypane.app/blog/always-open-localhost-in-your-development-browser/

However, "dev browser" for me actually means "private mode" in FireFox. Something sadly impossible in Finicky https://github.com/johnste/finicky/issues/49.

And disclaimer: Polypane who wrote the article is a paid browser (after 2 weeks). Wait -- that's a thing? Who knew?

ANSWER DISCOVERED: firefox "Always Open Privately" plugin does exactly what I want! https://addons.mozilla.org/en-US/firefox/addon/always-open-privately/ and https://github.com/fbausch/always-open-privately