Vertex hangs token counting off the model as its own path segment, and the
parser split the tail on the final colon alone. A count-tokens request
therefore reported its model as "claude-sonnet-5/count-tokens", which no
route claims, so the request denied as not-routable and the access log
recorded a model that does not exist.
Stop at the first "/" after the model id so the method segment stays out of
it, leaving the client free to price its context against the dedicated
endpoint instead of the billable inference one.