Connection of my domain to Google search console

Your domain for shortening URLs doesn't require connection to Google Search Console / Webmaster Tools.

Your main domain, and all URLs related to it, are 301 Redirected to other destinations. This means that you have already “told” Google that your shortened links have no standalone value, but only the destination pages do.

In that way, you cannot have a short URL ranked in Google. Your original links certainly have SEO value. If you use short branded links in articles, it will operate as if you did not have the intermediate step. It will pass nearly accurate the same amount of "link juice."