I'm in the transition from W7 to W10. For that purpose my machine is dual boot.
In W7 I just got the reminder to update my subscription and did so abut an h ago.
The program is not installed on C, but on H, hence accessible from both OS.
Now, when booting to W10 I get the same reminder.

Does the license depend on HW or OS?

It's a rhetoric question. The cost is low for a daily used application and hence I already have updated my subscription.

You should install the *same* license key on BOTH versions of Windows.