The error (BigQueryRelationProvider not a subtype) was caused by loading the BigQuery connector twice.
It comes pre-installed in Dataproc versions 2.1 and later, so there's no need to load it manually in this case.
The solution is to try removing the JAR used to create the cluster (spark-bigquery-connector-version=0.42.X) or recreate it without it, as I did.
After that, I was able to run the job.