Can someone point me in the right direction?
It looks like IAP was not fully installed correctly. Look for any remaining .unitypackage files in Assets/Plugins/UnityPurchasing and double click on each of them and go through the prompts. Compare to a brand new project also. If you get the prompt to Update the Unity API, have you made a backup? make sure to say Yes.
I tried a few different things, including your suggestions (there weren’t any .unitypackages in that directory). There definitely seems to be an issue that comes into play when I try to import https://assetstore.unity.com/packages/tools/integration/iap-manager-pro-iap-and-game-data-manager-77355
If I change of the order in which I import all these packages I can get to a point where there are namespace errors for UnityEngine.Purchasing. My assumption is that this is a related issue. The IAPManagerPro asset imports it’s own UnityPurchasing, could this be an issue? If I don’t import it, the namespace errors persist.
I’ve replicated my efforts in a clean project as well with the same results.
It’s at this point that all of these Assembly load errors start happening. I’m in a bit over my head for this one so I’m not sure if any additional random button clicking is going to produce positive results.
You would want to contact the developer for IAPManagerPro, it sounds like they need to update their package. I would suggest that you get the basics working first before trying to customize your game. Please start with the Sample IAP project and review the video. The errors that you have are not related to IAP, they are related to the UI component which has been moved into a Package Manager package in recent versions of Unity. https://discussions.unity.com/t/700293
I did play around with IAP before settling on grabbing an asset from the asset store. My entire purpose for this project is to build something using as much off the shelf solutions as possible to minimize costs for a client. I’ll see about contacting the developer for IAPManagerPro but in the mean time (who knows when they will respond) I’d like to fix the issue myself if possible. Also, I’ve already paid my $25 for the asset.
I doubt that you can, it looks they may be still using the previous UI component (if you have confirmed that the UI errors started after you imported their asset). I might suggest if you want to learn IAP, start with the Sample IAP Project here https://discussions.unity.com/t/700293 and the documentation here (for Google) https://docs.unity3d.com/Manual/UnityIAPGoogleConfiguration.html
I’ve already played around with IAP, have watched the Unity tutorials, AND have successfully written some scripts based on that. That’s not really the issue. None the less I’ve decided to roll my own solution despite already buying the IAPManagerPro asset (which I was only interested in for it’s in game currency feature).
I am, however, still a little bit confused by the fact that there seems to be two different Monetization solutions offered by Unity. What is the difference between In App Purchasing found in the Package Manager and the Unity Monetization asset that’s found on the Unity Asset Store? Also, are they incompatible? Both do seem to be maintained.
OH, by the way, those UI issues where from another Asset. That asset worked just fine until I started trying to install the IAP packages/assets. Not sure why they would suddenly break after installing unrelated Packages.
In App Purchasing is contained in the IAP package and Monetization includes Advertising. If you can provide specific steps to reproduce your issue on a new/empty project, we may be able to provide additional suggestions. But it sounds like you are unblocked now.
This is as far as I can get: “the update can not be completed because of the obsolete API, please update the obsolete API that you cannot update that is causing the errors before you update the obsolete API…” 
Please start with a new/empty project, and ensure that you can install IAP successfully. When you install IAP, you will get a pop up asking you to update the Unity API, you must say yes, as previously described here https://discussions.unity.com/t/776354/2
Unfortunately, this is a new/empty project. I did get the pop up and followed it’s instruction (said yes) without any issue.
The error happens when I import the IAPManger Asset. I’m monitoring this thread for answers as well:
Please reach out to the asset developer. As mentioned, it looks like they need to upgrade their syntax.
I could probably do it myself if I knew where to look. Converting their scripts to use the new API isn’t an issue for me but I have no clue what the equivalents are to look them up myself.
UnityEngine.Purchasing doesn’t exist in 2019.3. If someone told me what replaced it I could look up the API and make the changes myself in the time it seems to be taking for the asset creator to respond.
I might suggest then not to use their asset for now if it’s not working, we would not know what APIs they are using. But I suspect they are using the older UI namespace, and it’s since been moved into a Package Manager package. At any rate, just use Unity IAP as it is, many developers are doing just that. And yes, UnityEngine.Purchasing does indeed exist in 2019.3, I just confirmed. Please confirm yourself on a new/blank project, and import IAP.
No, I meant in the actual code. I have a Unity 2019.3 project, and it is recognized in my Using statements, etc. It’s there.