I continued to find online forums and guides to try and figure this out. I manage 2 websites and the first one only required a fresh install and reactivating it again. For the second one, I went through the Facebook Business side of the app and there is an option to install the Chat through that. I did that, it provided some Javascript SDK to put after the beginning <body> which I included into the theme, and it started working after that.
For others, I would recommend checking Facebook Business and going under the “Messenger” section till you find the install through that, and make sure you put in the code it provides.
