It would be good to see the cursor field which Airbyte selects for a connection.
I created the issue in Github to implement this feature https://github.com/airbytehq/airbyte/issues/15448
The reason that no cursor field is shown for streams on a CDC source is because CDC sources use a source-defined cursor, as CDC sources internally keep track of the current position in the replication log (see docs about that https://docs.airbyte.com/understanding-airbyte/cdc). Since they don’t use an actual column of the stream to do this, there is no “cursor field” set for those streams.
The reason that no cursor field is shown for streams on a CDC source is because CDC sources use a source-defined cursor, as CDC sources internally keep track of the current position in the replication log (see docs about that Change Data Capture (CDC) | Airbyte Documentation). Since they don’t use an actual column of the stream to do this, there is no “cursor field” set for those streams.
Also, a fix was merged in Show "source defined" as cursor for CDC streams, move strings to i18n by edmundito · Pull Request #16999 · airbytehq/airbyte · GitHub which is going to show as source-defined cursor to be more clear when you’re dealing with this situation.