Twitch all income has to be taxed?

How does the tax office want to find out that I earn money alongside Twitch, if that is not registered?

If you get it via Paypal, I think Paypal is just a bank…

There are different possibilities

Overseas tax on sales or VAT: Your data is deposited there for the purpose of payment. This data gets the tax office problem-free, because Twitch uses these naturally profit-reducing as operating expenditure. So they are flowing there, must have flowed somewhere. Do you know the saying from thrillers: "Follow the money"?
Your bank account. The tax office can quite arousing glance at any time and then see the yes if there money flowing.

You are logged in to Twitch. And since Twitch posts the payments to you, the tax office knows your revenue.