“Not your keys, not your coins,” as the saying goes. The app may owe you bitcoin, but you don’t truly own it until it’s stored in a wallet controlled by your secret key. This situation might actually be a blessing in disguise, encouraging you to ensure your wallet is set up to transfer your sats from the app’s custody to your private one. (It sounds like you’re already on this path, given your sign-up with the Bitcoin Way service.)
If I were in your position, I’d contact the app representative to understand their reasoning behind this decision and whether they might ultimately release your funds. It’s worth noting that blockchain surveillance companies often score wallet addresses based on their “risk profile.” These scores can sometimes be inaccurate, associating addresses with suspicious entities due to interactions further down the chain of transactions. If the address you sent your bitcoin to has been flagged this way, it could be the cause of the issue.
Explain to the app representative that you are simply paying for a completely legal service and provide evidence to support this. This might persuade them to release your bitcoin.
If they still object, but you’re able to settle the debt they owe you via fiat currency, it might be worth doing so. You could then use the equivalent amount (minus fees) to purchase bitcoin through alternative means—either privately (no KYC) or through reputable vendors (with KYC). This time, ensure that the bitcoin is sent directly to your private wallet under your control.
I hope this helps!