There is no device limit. You can use your licence on your desktop, your laptop and any other computer you use. This article used to describe a two-device cap from an older version of the plugin; that no longer applies.
What your licence does limit
The number of people who use it (seats). Solo is for 1 person, Agency for up to 5, and Enterprise is priced per person with a minimum of 6. WordPress sites are unlimited on every plan.
What the plugin sends us
Only a licence check: when you activate the plugin, and about once a week after that, your site sends your licence key and your site’s address. There is no machine ID and nothing is tracked per computer.
Using it on a new computer
Nothing to do on our side. Add your website as a connector in Claude on the new computer and sign in to your site when it asks. See How to connect your WordPress site.