The solution is to use VNC viewer/server to connect to your host unattended machine. VNC allows you to disable the proxy, making it seem like you are physically on the server to mimic the behaviour of unattended mode.
With VNC, this is done via File > Preferences > proxy > do not use a proxy.
Let's say you have an Azure VM that you will use to run unattended flows. This is your host. When you use Microsoft Remote Desktop to connect to the host, you have a client device (your own laptop, desktop, workstation) that also serves as as a proxy for the traffic going to the host.
When you run an unattended flow, there is no proxy - it's being run on directly on the host. It's as if someone is physically using the machine.
My particular problem was that our in house application registers information about the device accessing it. When using RDP to build he flow, it registered my laptop. This registration is done only the first time through a prompt that won't appear again. So, my laptop was registered and I proceeded to build the flow not accounting for this registration process.
When I tried to use the flow in unattended mode, the Azure VM host hadn't been registered before and thus there were prompts on the screen that my flow couldn't handle.
Thanks to @Henrik_M I incorporated screenshots into my flow to see that this was happening.
Once I got that sorted out I did have to add additional waits into the flow before a few specific button press actions - these waits are not necessary in attended mode but for some reason are in unattended.
