For anyone struggling with this, here is some helpful information:
This is a thread describing the process of updating your project after you've updated the engine itself (they both have to be done):
https://forums.rpgmakerweb.com/index.php?threads/rpg-maker-mv-v1-3-5-update.74891/
MAKE SURE YOU BACKUP YOUR PROJECT ELSEWHERE FIRST
The problem with this thread is that no one has 100% predictive power as to whether or not this process will still work for each subsequent update, or whether it will work with your specific project due to the unique list of plugins that you might be using.
Which brings me to my next point. Plugins (at least in some cases) will also have to be updated. Very important plugins like the Yanfly core engine are a perfect example as not updating these can be game breaking.
As such you should grab the latest version of these plugins and drop them into your project's plugin folder (
making sure to back up the previous versions first).
At this point there is the issue of getting the new versions of the plugins to load. RPG Maker MV's plugin feature does not audit the plugin folder on each use so you have to load each new plugin manually. Yanfly has a good video about how to do this but I'll explain it here since it's simple:
After placing a new plugin in the plugin folder load the engine and open the plugin list. Find the plugin you want to update in your list of in-use plugins. You'll notice that the version number (for those that have it) is still the old one. In order to get the new version to initialize and stop using the old one you simply need to double click on it the way you would if you where going to access its parameters. In the parameters you will see the new version number at the top. Now all you have to do is exit the parameters for that plugin and you see that it's also updated in your list. This is how you manually update individual plugins, and when you update your engine and project hopefully there are only a couple offending plugins that cause errors.
If you attempt this process put experience too many issues (as in the case of a very robust project) you may feel safer just reverting to the version of the engine you were previously using and reloading your backup project. In order to do this you simply need to click on RPG Maker MV in Steam
(go to your library, hover the mouse over the library tab again, a drop down menu will appear, click on "software", and that's where it will be listed). Now right-click on RPG Maker MV and select "properties". When the menu pops up click on the "betas" tab, then use the drop down menu labeled "select the beta you would like to opt into" and choose the version you were previously using. Performing this step and reversing all the other steps will bring you back to square one. This can be used in the event updating everything doesn't work, and exists just for such an instance regardless of how "elementary" some people make this process seem. The important thing is not losing your project, right? 
Original thread:
https://forums.rpgmakerweb.com/index.php?threads/steam-version-way-to-get-to-an-older-version.91656/
I've placed this information here because it was something I had issues with. Different people with unique projects might experience different hiccups when attempting to update a project, and not all of this information was in a single thread. Hopefully this helps some people that are new to this sort of thing!