iPhoto Library disappeared from Mojave

You won't be able to.

The Screensaver Preferences will only allow you to

choose the photoslibrary from Photos

As said Apple deprecated iPhoto in favour of Photos.

If you open iPhoto and select the images you want to use as a screensaver

you can export them to a folder on your Desktop or wherever you want.

Open the Screensaver Preferences and click on Source and select

Choose Folder… from the next window you can navigate to your folder of images

and select it.

Or you could open Photos and import your folder of images and then in Screensaver Preferences

at Source select Photo Library…

Locate your old iPhoto Library that you had been using for displaying the images like your Boss had wanted. Make a copy of it. CONTROL-click on the copy and tell it to open using Photos. If this works, that iPhoto Library copy will be migrated into Photos. Then you can hopefully use that Photos Library for your screensaver. Maybe make the Boss happy.

If the above does not work, here is something else you can look into. CONTROL-click on your iPhoto Library, and select Show Package contents. One of the folders there is very large and contains all the photo image files, it might be called Masters, or it might have a different name. The one you want should be large and contain numerous nested folders with names like numbers, dates, or letters. Inside these folders are your actual photos.

Once you know where these folders are, take note of the highest level one.

Then open Photos holding down the option key, to create a brand new empty Photos Library. Select File => Import and select the previously identified highest level folder in the old iPhoto Library with all those photos. Look for a check box or option to preserve folder structure. This should import all the photos from your old iPhoto Library into a new Photos Library.

Now you can use this Photos Library with the screensaver. If the Boss is still around, waiting patiently to be made happy, maybe you can declare victory and score important points with said Boss.

So I am now thinking there is something wrong with your Mojave installation. How you followed these instructions:

https://support.apple.com/guide/mac-help/use-a-screen-saver-mchl4b68853d/10.14/mac/10.14

It clearly describes how to select a Photos Library for your screen saver. This should work. It works on my Macs running El Capitan, High Sierra, and Catalina (I can't test directly in Mojave as I don't have a Mac running Mojave right now). The fact that this is not available to you on your system makes me suspect something is not right with your installation. The way you brought in a boot drive from a different model Mac in might or might not explain why something is not right. Are you following the exact steps outlined in the above Apple support article? (By the way, I also created a plain folder on my desktop and exported some images to it, I could also select that folder for the images to display for the screen saver.)

If this is your only anomaly, maybe you can live with it. Since you have an older Mac that can't go past Mojave, this is the latest OS you can run on it so you don't need to worry about future upgrades going south. If it were me, I would make several complete backups and would do the clean install, I have done that multiple times and am comfortable with it, but not everyone is at ease with that.

The "failing" SSD notice referred I believe to your boot drive. In the second report, it did not say "failing" anymore but noted "poor SSD performance." You could certainly check that SSD with DriveDX or TechTool Pro to get more info. DriveDX provides the best assessment of how much life is left in an SSD. It also provides in depth details on all the individual SMART parameters.

There was some software called "Appcleaner" in there that I would stay away from.

Anything more than 4 or 5 years old is considered "vintage." I'm typing right now on a 2008 iMac running El Capitan (which is as far as it will go). It works great, with an SSD and just 4 GB RAM. But I have also noticed a number of web sites not loading properly in Safari (they do work ok so far in Chrome) and also some emails don't display right with that old version of Apple Mail.

I don't think any of the issues found by Etrecheck are impacting your ability to display Photos images in the screen saver. Which was what you really were interested in. For that, I think you need to designate the appropriate Photos Library as a System Library and then try again. I certainly did not see some sort of photo utility installed that would interfere with that simple function.

If it still doesn't do what you want, maybe this was already tried, but have you booted into safe mode and tried there, or tried from a different user (just create a new Admin user for this test)? Have you ever run Appcleaner? Sometimes these "cleaners" remove operating system files that result in odd behaviors. I think you sound way too savvy to have done that, but just asking.

if the version of iPhoto was older than 9.6.1 prior to the upgrade to Mojave, then it will be unusable and its icon will be marked with a circle and a slash. There is no means to get iPhoto to v9.6.1. If it was v9.6.1, then the Mojave upgrade process would not have removed the application. I still have iPhoto v9.6.1 on my Mojave installation.

I'm perplexed with what you are experiencing because on my computer running El Capitan (2008 iMac, that's the highest OS it can run) and also on my Catalina Macs, the screen saver shows the Photos Library as an option for the screen saver slide show.

On the El Capitan iMac, it even allows me to select an iPhoto Library or a Photos Library for the slideshows, I can change back and forth.

I don't have any computer currently on Mojave right now to test, however.

Maybe create a little test Photos Library in your home Pictures folder with a small number of photos in it and see if that works? I am wondering if locating the Library in a shared folder on another drive is somehow affecting what you are trying to do.

Your setup looks a bit complex!

In any case, as I said, I suspect something with your Mojave installation, as you inherited it from a disk that had been used on a different model. While you have been using it and it boots, sometimes the MacOS has custom features for different hardware on different Macs. Your 5,1 hardware is different from the 3,1 hardware, especially graphics cards and drivers. It might (or might not) be related to your issue. It bother me because you just want to do something that is a pretty basic advertised feature of the MacOS, the fact that it does not work for you is a symptom of something incompatible.

If none of this troubleshooting appeals to you, you can simply live with what you have and set up a slideshow running all the time using iPhoto or Photos (or something else, there are many programs that will do that) independent of the screen saver.

You could also run Etrecheck (use it with permission to have full access to your machine; it is a trusted utility that a respected developer provides for free) and post the output into a message here. Lots of people here are pretty skilled in finding incompatible extensions and software listed in Etrecheck (I will also look but am not as experienced as many others who check in on these discussions), there could be a very simple answer and solution here. Also, having any anti-virus or "cleanser" programs/software is a big no-no, they create conflicts all the time, well documented in these forums.

iPhoto was replaced by Photos; I can't recall exactly when.

You will probably find there's a Photos Library.photoslibrary in your ~/Pictures folder.

I could be wrong though!

The screen saver can only detect the Photos Library in Mojave, and will not even play my old iPhoto slideshow. Price of progress.

P.S. Going back to your very first post in this thread,

"Just updated to a Mac Pro 5,1 from my 3,1 and Mojave.

Just moved the HDD's over to the new box and then updated the OS."

You said you moved the HDD's over to the new box and updated the OS. Does that mean that you started from the boot drive from the 3,1 Mac Pro and started using it as the boot drive on the 5,1 Mac Pro? Not sure how well that would work, those are two different models of Mac Pro, with different internal hardware, include different graphics cards. In the old days, one could use a universal MacOS to boot any Mac and it would run and function properly, but nowadays supposedly using a MacOS for one Mac model to run a different Mac model can lead to unexpected behaviors.

Maybe that's not what you did, however ... Maybe when you said you moved the HDD's over you meant just the data drives, not the boot drive?