Avoiding is almost impossible, discouraging is the strategy.
1. move you extension to mozilla addon store.
Mozilla permits to upload obfuscated addon
as long as it is also uploaded an clear version with the exact instructions to build the obfuscated one.
Of course, if review process will succed, only obfuiscated version will be pubblished.
(Maybe the MS-Edge store does the same too - I have not verified)
2. Let the extension communicates with your own server just with simple post message(s) which permits server to acknowledge the original extension
and ban the "competing" extensions.
Better if in that message you include a field with a kind of apikey that your users will only get after a sign-in phase.
At this point if you notice fraudolent network traffic (i.e several network request from same apikey with many different ip address in a predefined time frame)
you can ban that apikey.
Mine are just tips, now it's up to you to decide how much time and\or money to invest to make your extension (or your business) safer