Was backup start time intentionally omitted from pg_stat_progress_basebackup, or would it be okay for me or someone else to add it as a column? Or, am I being daft and there is another obvious way to get the start time for an in-progress base backup?
Not sure about base backup but the other progress reporting commands would get that info from pg_stat_activity.query_start which can be joined to using pid. backend_start is likely close enough for pg_basebackup if it doesn’t recognize the replication protocol as a “command”. I haven’t checked.