Unfortunately this doesn't look like an Airbyte issue - even though your API token is correct, the Zendesk account doesn't have the correct permissions enabled. I searched and can't find a tutorial to enable this particular access feature, so I'd advise contacting Zendesk support directly:
https://support.zendesk.com/hc/en-us/sections/4405298846618
Does this error come up when you are setting up the connection?