@katherinejoyceO believe it or not, but you actually just indirectly helped me solve the problem. The link you gave for the Connect With Square app allowed me to access that app's installation. That is the older app which is no longer supported since Sync With Square was introduced. Allowing me to connect the old app triggered something behind the scenes that fixed the problem for me. 

For anyone else who has this issue, this is what I did to solve it.

• Go to the Connect With Square app page. 
• Follow the instructions to connect the old square app (Connect With Square)
• Once it connected, a window popped up in Quickbooks Online asking me to stop using the old app and to disconnect it. There was a disconnect button at the bottom of the pop up that I used to do this.
• Once that is done, I went back to my App Transactions tab where it still showed Square was not connected.
• I clicked the button to install Square on this screen, which brought me to the Sync With Square app page. 
• I clicked the button to install and followed the prompts. This time I did not error out and successfully connected Square to Quickbooks Online again.
• I made sure to let the syncing process take its time and to not interrupt it. Everything is working the way it used to so far!