What permissions does a Codeberg access token need?

For most people, none at all. GitHub Store only reads information from Codeberg, so you don't need a token just to browse public projects. Adding one simply lets you browse more before Codeberg's rate limits slow you down.

You only need a token if you want GitHub Store to show your private repositories. To create one, go to Codeberg → Settings → Applications, generate a new token, and tick read:repository. If the private repository belongs to an organization, also tick read:organization.

That's everything it needs. GitHub Store never asks for permission to change anything in your account — only to read.