OK Old Toad and Leonie, here's the update. Following your feedback I waited another day and then checked both the hard drive and the Photos Library size again on August 25. Indeed, these had updated and reflected an increase in hard drive space likely the total GB's of the files deleted some days earlier. So it would appear that "sometimes" the library takes a long time to reflect the change in size as a result of the files deleted. I must point out though, that on August 25, I deleted another set of photos and videos, this time carefully recording the number of files and sizes so that I could determine how long it would take to update the changes in the Photos Library size. To my surprise, the changes were reflected a few minutes later. I double checked the number of files in the Photos App and the photos library, as suggested by leonie, and confirmed that both had been updated correctly. Thankfully I did not need to reindex Spotlight.
One other observation that perhaps helps to explain this anomaly. Yesterday, before I did any of the above, my iMac crashed twice and rebooted. I then did a manual shutdown. I don't normally shutdown my computer daily so perhaps this explains why the Photos Library and the info on the Hard Drive memory updated after I restarted the computer. This may be another useful step to follow for anyone having issues with the the Photos Library not updating when files are deleted.
Thanks for your feedback in helping to resolve this issue.