No, Stack Overflow doesn't update the Last Seen value from your network profile; otherwise my Linguistics profile would reflect my activity on SO and not that I rarely visit that SE site.

The consecutive days metric requires more than a mere visit to count a day as active. You need to do more than that; loading any page on Stack Overflow while logged in will count as a visit, but to count as active you need to do more than that. What exactly, is not public to prevent gaming of the Enthusiast and Fanatic badges.

You probably opened a single page on Stack Overflow somewhere(or perhaps opened the mobile app or had a page open in a mobile browser that then reloaded automatically) that day, nothing more. You visited, but were not active.

No, Stack Overflow doesn't update the Last Seen value from any other site. Visiting Meta.SE does not count as a visit to Stack Overflow. Your visit times don't match exactly, which is what you'd expect if a visit to one was counted towards another site too.

The consecutive days metric requires more than a mere visit to count a day as active. You need to do more than that; loading any page on Stack Overflow while logged in will count as a visit, but to count as active you need to do more than that. What exactly, is not public to prevent gaming of the Enthusiast and Fanatic badges.

You probably opened a single page on Stack Overflow somewhere  (or perhaps opened the mobile app or had a page open in a mobile browser that then reloaded automatically) that day, nothing more. You visited, but were not active.