That's plain false. With a VPN enabled, the ISP can see data volume and time stamps, and what VPN server you're connected to. Nothing else.
Your browser, depends on the browser. Chrome, Edge, etc., yeah, they're watching everything you do. An open-source privacy-focused browser with maximum privacy settings enabled is not watching as much, if anything at all.
And incognito doesn't hide your fingerprint from search engines or websites. It's basically worthless for privacy. All it does is clear cookies, caches, and browsing history from the local device.