Or do it a bit like the engagement factor was for autoplay. A site gets an extended interval before clearing because it receives user interaction and the user spends X minutes on it. I'd actually be fine with sites that receive no user interaction or the user spends less than 1 minute on having immediate evacuation of storage when the user leaves.
I don't think gating on interaction does much of what they want, because they are trying to prevent cross-site tracking and it is quite common for people to interact with both sites.
This is a mitigation that specifically addresses tracking that runs entirely on the client. If you set a cookie from the server the time limit does not apply, which means you can store whatever information you want on the server keyed by an HTTP cookie.
