Looks like it should be good, deleting every night at midnight.
If you want to see what will be deleted just run the find part:
/bin/find /usr/local/webhelpdesk/pgsql19/Backups -type f -mtime +7
always a prudent idea. Run the script in "safe" mode to find out what is is going to output. Then when you are sure, go ahead and implement the rest of the script. You may want to actually run it in the shell before you enable it in the CRONTAB just to be sure what it is going to do. Just my two cents.....
Also, you may want to investigate the rotatelogs concept. Whereby, given the log reaches certain parameters that the logs are automatically closed and compressed and then a new log file opened up. That way the logs are available for a longer period of times.