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We found we only needed read_repositry permission when we setup a recent job. We use Gitlab - to test we checked it worked from the cluster by running -

curl -sS -u '<gitlab-token-username>:<gitlab-token-value>' \
  '<HTTPS://REPOADDRESS>' \
  | head

That asserted the cluster to see the repo with our credentials, no idea why your seeing Write access issue... Our secret was created with -

kubectl -n fleet-default create secret generic <xxx-git-auth> \
  --type=<http://kubernetes.io/basic-auth|kubernetes.io/basic-auth> \
  --from-literal=username='<gitlab-token-username>' \
  --from-literal=password='<gitlab-token-value>'

kubernetes.io/basic-auth example above - you may want kubernetes.io/ssh-auth instead... good luck