Answer: Make sure you are actually using Exchange Online before trying to run Exchange Online commands
As mentioned before, I am new to Exchange/Exchange Online and for that matter, to my current company. I very much appreciate the responses here.
I have found that I was mistaken on thinking we were using Exchange Online. We actually are hosting Exchange on prem. I found that I can get onto the local exchange server, and open the "Exchange Management Shell" and I am able to type the commands in that @Yuki Sun-MSFT mentioned and they are working as I expected. This was the information I was originally after.
I have also found that you can use this link:
to create a remote session and run the old non-EXO commands as well from my local workstation.
As disappointed as I am with not knowing the facts before posting this thread, you all have sparked many more questions about these technologies (Azure AD, Exchange Online, Exchange Server) which will encourage me to pursue further knowledge in these areas of IT as well, which as we all know is half the fun of being in IT! Thank you guys again.