Streaming despite a full-time job?

Unfortunately I'm not the fittest from a tax point of view. How does it work if you stream on Twitch in addition to your full-time job (40h week) and are invited to become an affiliate. A trade has to be registered, that is clear to me. But what kind. Sole proprietorship? Small business owners? How is the whole thing taxed? With my main activity I'm above the tax allowance, i.e. All twitch income must be fully taxed? Can something change in my tax class or health insurance. If anyone has any experience with this, please let me know.

But what kind. Sole proprietorship? Small business owners? How is the whole thing taxed?

That depends on how much sales you will make.
If you are sure that you will not have a turnover of 22,500 euro in the 1st year, you can register it as a small business - sideline. You do not have to pay taxes or pay anything to the tax office. An EÜR is then submitted to the tax office every year.

Can something change in my tax class or health insurance.

Not at first. But you don't have to participate in the affiliate program either, that's up to you. But remember: Profit intention = business! Regardless of whether you are an affiliate.

First of all, thank you very much for the information. Does the 22,500 euro turnover only apply to Twitch or does it include my current salary as well?

They apply to your business.