SCRIPT: Check if Full backups executed in last 7 days

 SELECT ROW_NUMBER() OVER(ORDER BY d.name ASC) AS rownum, d.name, MAX(b.backup_finish_date)
FROM master.sys.databases d
    LEFT OUTER JOIN msdb.dbo.backupset b
        ON d.name COLLATE SQL_Latin1_General_CP1_CI_AS = b.database_name COLLATE SQL_Latin1_General_CP1_CI_AS
           AND b.type = 'D'
           AND b.server_name = SERVERPROPERTY('ServerName') /*Backupset ran on current server */
    LEFT OUTER JOIN msdb.dbo.backupmediafamily f
        ON f.media_set_id = b.media_set_id
        AND b.is_copy_only = 0 -- to avoid VM snapshots
WHERE d.database_id > 4 AND d.name NOT IN ('Dbatools', 'ReportServerTempDB', 'DWConfiguration', 'DWDiagnostics', 'DWQueue')
      AND d.state NOT IN ( 1, 6, 10 ) /* Not currently offline or restoring, like log shipping databases */
      AND d.is_in_standby = 0 /* Not a log shipping target database */
      AND d.source_database_id IS NULL /* Excludes database snapshots */
         AND D.state_desc = 'ONLINE'
GROUP BY d.name
HAVING MAX(b.backup_finish_date) <= DATEADD(dd, -7, GETDATE())
       OR MAX(b.backup_finish_date) IS NULL