Hi @Ivan.L
I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue:
Azure Function App fails to deploy using CI/CD: GitHub
Solution:
Deleting and recreating the Function App fixed the issue.
Creating new app resets the IAM settings and may result in prompting to assign the roles again.
And also new app creates a new Identity binding which might have helped to resolve the issue.
You can check the role assignments using the Azure CLI
az role assignment list --assignee ManagedIdentyClientID --all
Please click Accept Answer and kindly upvote it so that other people who faces similar issue may get benefitted from it.