What breaks, and what to do about it
Three things stop working as browsers restrict third-party cookies. Cross-domain user recognition — the same person on your marketing site and your app on a different domain — becomes two people. View-through attribution largely disappears. And any embedded tool that relied on recognising a returning visitor from another origin loses that ability.
The replacements are first-party and server-side. A first-party cookie set by your own domain is unaffected. Server-side tagging moves the identification off the browser entirely. Consent-based first-party identifiers work where you have a logged-in relationship.
What does not work is patching around it — the alternatives that attempted to recreate cross-site recognition through fingerprinting are explicitly targeted by the same browser policies, and by privacy regulation that is moving faster than either.