I use Finicky to seamlessly route links to the right place (browsers and apps, such as Zoom so you don't have to bounce in a browser then the app).
You can use the args param in the browser callback to get incognito mode for your matches (I've confirmed this snippet works for Brave; others may vary):
browser: ({ urlString }) => ({ name: 'Brave Browser', args: ['-incognito', urlString], }),