After encountering an issue with the latest update of Age of Empires (AoE) not opening for me, I contacted their support team and found out the game no longer supports Windows 7.
Following some instructions from an older post, I was able to download a Windows 7 compatible version of the game from February 6, 2023.
To do this, I first installed Dotnet 6.0 and DepotDownloader, then I ran a series of commands to download the version prior to the current one.
After that, I copied the newly downloaded game folder to the Steam library and was able to launch the game from there.
I hope this helps someone else who is facing the same issue.