@Siegfried Heintze Thanks for reaching out to Microsoft Q&A, apologize for any inconvenience caused on this.
To repro this behavior, I have created an app service and tried to deploy the code by adding the source control using the cmdlet. I am able to link deploy the source code from the repo successfully as well.
az webapp deployment source config -g <resource-groupname> -n <WebAppName> --repo-url <GithubUrl> --branch <BranchName> --manual-integration
As per the cmdlet documentation of az webapp deployment source config --git-token
parameter is not a mandatory/required parameter, and this should not break the operation as well.
Also, --git-token property is not required for the public repositories and the shared cmdlet operation might be failed because of a different reason.
I would suggest you try using the above shared cmdlet or try running your cmdlet in debug mode by appending --debug at the end.
Let me know if you are still facing the issue or if you have any further questions on this.