Privacy
What the extension sends here
When you activate a licence, the extension sends the licence key you typed and a random identifier it generated for that installation. Nothing else. It repeats that check every few days to confirm the licence is still valid.
What is stored
Against your licence: the email address you paid with, which Stripe provides; the identifier of each device you activated, when it was added and when it last checked in; and the network address those checks came from.
What the extension does not send
Describe this precisely and keep it true. Pages you visit, page contents, what you type, and browsing history are the four things to be explicit about.
Payments
Card details go to Stripe and never reach this server. This server records that a payment happened, the amount, and the email on the receipt.
Deleting it
Removing a device from your account page deletes its record. Ask, by replying to your receipt, to have the whole licence and its email address removed.