Someone on r/IBMi was able to figure out, what was wrong. In short, the RSA-PSS in generating the cert.pem was the issue. In the documentation for the API it explicitly shows this command and explicitly says multiple times use the RSA256.

Therefore, I selected the RS256 option on jwt.io and ofc that has the wrong format. And that was it. Here the Thread of the reddit to figure out what was wrong: r/IBMi