So, in about 1 hour my extensions failed hard.
I was doing my extension and it was doing what I pretended. I made some changes, and as I didnt liked I deleted them,
You can also relax your CSP for styles by adding style-src 'self' 'unsafe-inline';
"content_security_policy": "default-src 'self' style-src 'self' 'unsafe-inline';"
This will allow you to keep using inline style in your extension.
As others have pointed out, this is not recommended, and you should put all your CSS in a dedicated file. See the OWASP explanation on why CSS can be a vector for attacks (kudos to @ KayakinKoder for the link).