but would Codeberg's policies allow doing such thing ?

In its terms of use, Codeberg explicitly outlines under what license terms it provides code hosted on it:

• the right to use the content for any purpose, including both commercial and non-commercial purposes
• the right to make unlimited copies of the content and redistribute those copies to others, with or without charge
• the right to examine the content and determine how it works and/or how it was made
• the right to make their own modifications to the content, to use the content with those modifications privately
• and the right to redistribute copies of the content which include their own modifications, with or without charge

You are not allowed to upload code which you do not have permission to publish under these terms. Which means you can't just arbitrarily relicense code you got from Github, and you also can't upload Github projects with a more restrictive license, such as non-commercial ones.