Thanks Neil22R for the comprehensive response. I have tried the Safe Boot and have even reinstalled Ventura from the Recovery Mode. The issues, as I understand them, are that my external monitor no longer shows in Screensaver Settings, but does under Wallpaper Settings. Secondly, using the Activity Monitor, I noted that, after leaving the screensaver mode "iLife Slideshows (Screensaver)" is shown as an activity for a few seconds, then disappears. It is activated by "Launchd" when I mouse over to the hot corner to activate the screensaver. The screensavers are controlled on my iMac under Ventura/System/Library/Screensavers. That folder is protected within the System, so I can't use Time Machine to replace it with a previous working folder.
There are a number of other discussions concerning this fault after the update to Ventura 13.3, all happening with external monitors. If I disconnect my 27 inch AOC external monitor, the problem goes away and the iMac shows my photos just fine. I wrote up a bug report and anticipate there will eventually be a fix, just as there was previously with Big Sur.
My external monitor is connected via a Thunderbolt to DisplayPort cable. I have found that to use TimeMachine to recover files, I have to disconnect or switch off the external monitor. That may be the source of the problem.
So now, my photos are shown as Wallpaper and iTunes/Music Albums are shown as a Screensaver. Such is life.