How does connecting to your own wifi fingerprint your computer?

I sometimes hear about hackers who get caught because they let their computer they did something malicious on get connected to their home network, but I don't quite understand how this works.

Let's say we have a new install on a laptop and take it to a mcdonald's, and that's the first time it's ever connected to the web. The attacker does their job there and when they go home, having not logged into anything or done any fingerprinting activities, …

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