No, the update script explicitly creates the new folder with the required permissions.
But you may have a point, in the unlikely event that it wasn't Pi-hole creating that folder:
One possible explanation for your observation would be that you've created that folder manually.
This has been suggested in FTL log move error during latest update (Pi-hole FTL v5.16, Web v5.13 and Core v5.11.1) - #6 by yubiuser as a workaround for a glitch that was introduced by an early Pi-hole FTL v5.16, Web v5.13 and Core v5.11.1 released, which has since been addressed in the meantime.
Did you perhaps apply that workaround and create the folder manually, perhaps while logged in as root?
No again - the update process takes care of rights and permissions.
As suggested by our update note, running pihole -up is enough - no need to switch to another user:
