Нашла следующие возможные исправления

Поменять elog(VERBOSE..) на LOG:
(Переименование файлов тоже под elog(LOG..) должно быть)

src/restore.c
846:elog(VERBOSE, "Create external directory "%s"", dirpath);
926:elog(VERBOSE, "Deleted file "%s"", fullpath);

src/merge.c
813:elog(VERBOSE, "Deleted "%s"", full_file_path);
1147:elog(VERBOSE, "Deleted "%s"", full_path);
1196:elog(VERBOSE, "Rename %s to %s", old_path, new_path);

src/backup.c
415:elog(VERBOSE, "Create directory '%s'", dirpath);
2067:elog(VERBOSE, "Skipping the unchanged file: "%s"", from_fullpath);
2071:elog(VERBOSE, "File "%s". Copied "INT64_FORMAT " bytes",

src/dir.c
1137:elog(VERBOSE, "Create directory "%s" and symbolic link "%s"",
1154:elog(VERBOSE, "Create directory "%s"", dir->rel_path);
1892:elog(VERBOSE, "Deleted file "%s"", fullpath);

src/archive.c
364:elog(VERBOSE, "Rename "%s" to "%s"", wal_file_ready, wal_file_done);

Поменять elog(LOG..) на INFO (скорее всего):

src/backup.c
119:elog(LOG, "Database backup start");
339:elog(LOG, "Current Start LSN: %X/%X, TLI: %X",
343:elog(LOG, "Parent Start LSN: %X/%X, TLI: %X",
676:elog(LOG, "This PostgreSQL instance was initialized with data block checksums. "
743:elog(LOG, "Backup destination is initialized");
1516:elog(LOG, "stop_lsn: %X/%X",

Поменять elog(INFO..) на что-то другое:

src/util.c
592:elog(INFO, " block %u", blocknum); -- здесь инфа по блокам, VERBOSE

src/data.c
1767:elog(INFO, "Block %u of "%s" is truncated",

Исправил по замечаниям ревью, внёс изменения и для других команд (не только для catchup)

Новая партия предложенных правок

(аналогичные сообщения стоят под VERBOSE)

Поменять на VERBOSE (информация по блокам, тредам, WAL):

src/backup.c
1274:elog(LOG, "Looking for segment: %s", wal_segment);
1276:elog(LOG, "Looking for LSN %X/%X in segment: %s",
1297:elog(LOG, "Found compressed WAL segment: %s", wal_segment_path);
1301:elog(LOG, "Found WAL segment: %s", wal_segment_path);
1318:elog(LOG, "Found LSN: %X/%X", (uint32) (target_lsn >> 32), (uint32) target_lsn);
1347:elog(LOG, "Found prior LSN: %X/%X",
1415:elog(LOG, "Invalid offset in stop_lsn value %X/%X, trying to fix",

src/data.c
1838:elog(LOG, "File "%s", block %u, page is NULL", file->rel_path, blknum);
1841:elog(LOG, "File: %s blknum %u, empty zeroed page", file->rel_path, blknum);

src/archive.c
470:elog(LOG, "Temp WAL file already exists, waiting on it %u seconds: "%s"",
499:elog(LOG, "Reusing stale temp WAL file "%s"", to_fullpath_part);
520:elog(LOG, "WAL file already exists in archive with the same "
531:elog(LOG, "WAL file already exists in archive with "
716:elog(LOG, "Temp WAL file already exists, waiting on it %u seconds: "%s"",
745:elog(LOG, "Reusing stale temp WAL file "%s"", to_fullpath_gz_part);
769:elog(LOG, "WAL file already exists in archive with the same "
780:elog(LOG, "WAL file already exists in archive with "
1165:elog(LOG, "Failed to get WAL file %s, retry %i/3", wal_file_name, fail_count);
1240:elog(LOG, "Thread [%d]: Failed to prefetch WAL segment %s", 0, xlogfile->name);
1317:elog(LOG, "Failed to prefetch WAL segment %s", xlogfile->name);
1449:elog(LOG, "Target WAL file is missing: %s", filename);
1489:elog(LOG, "WAL file successfully %s: %s",
1663:elog(LOG, "Prefetched WAL segment %s is invalid, cannot use it", wal_file_name);

src/parsexlog.c
691:elog(LOG, "First record in WAL segment "%s": %X/%X", wal_segment,
787:elog(LOG, "Record %X/%X is next after target LSN %X/%X",
913:elog(LOG, "Record %X/%X has endpoint %X/%X which is equal or greater than requested LSN %X/%X",
1039:elog(LOG, "Thread [%d]: Opening WAL segment "%s"",
1058:elog(LOG, "Thread [%d]: Opening compressed WAL segment "%s"",
1491:elog(LOG, "Thread [%d]: Endpoint %X/%X is not inclusive, switch to the next timeline",

src/stream.c
248:elog(LOG, "started streaming WAL at %X/%X (timeline %u) using%s slot %s",
258:elog(LOG, "started streaming WAL at %X/%X (timeline %u)",
340:elog(LOG, "finished streaming WAL at %X/%X (timeline %u)",
393:elog(LOG, _("switched to timeline %u at %X/%X\n"),

src/data.c
1767:elog(INFO, "Block %u of "%s" is truncated",

Посмотрел последний комментарий@MetalDream666 (и указанный там код), но ничего не стал менять в коде, по одной из двух встречающихся причин:

1. некоторые сообщения уже были VERBOSE
2. WAL segment -- это файл, соответственно уровень логирования -- не ниже LOG, а чаще даже информация касается общего процесса выполнения (например обработка в команде archive_push)