The same way users can modify the storage, they can also modify the extension's payment checking function to always return "paid".
There is no fool-proof licensing system for client-side (offline) extensions.
You could try to implement some obfuscation techniques that make it harder to bypass, but you can't make it impossible to bypass.

As Mozilla recommends in "Make money from browser extensions":

Developer Tip: Do not spend too much time securing your licensing system against hackers, because users who are inclined to use a hacked license are unlikely to pay for one. Your time is better spent developing new extension features that attract more paying users.