Minimum permissions required by the application
Publish requires a certain level of permission that you must grant via the application previously registered in AzureAD.
The definition of permissions can be found here: https://learn.microsoft.com/en-us/sharepoint/dev/solution-guidance/security-apponly-azuread
It is strictly necessary to have a Reading/Writing.
The definition can be done on all sites (Sites.ReadWrite.All) or only on selected sites (Selected Sites)