The wallet works even if you provide false information about your identity.
If Strike took your sats just because you provided wrong information about your identity, its owners would be committing several crimes, including abuse of trust and fraud. What's more, neither Strike nor Primal ever inform the consumer that their wallet won't work if the information entered isn't true. Don't forget that one of the supposed advantages of bitcoin transactions is that they protect anonymity...
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They don't take your sats, they permanently disable your ability to use Strike forever. It's not Strike's fault, it is because they did a deal with the devil to support fiat. Cash app and River same thing.
I mean when they ban you, not saying they are banning you by providing false info, I am just curious how you can use a KYC backend (Strike) without full KYC. If that works, I'm sure the feds will close that "loophole" soon enough.
Only thing you need to do is transferring your Nostr sats to your bitcoin wallet. Even Primal app allows you to do that.