I ran into the exact same problem today but I was able to put together a workaround. Note that this prompt comes up when the desktop flow needs to authenticate with a cloud platform, even though it already has for some weird reason. We have another computer running a localized flow with no cloud account interaction that doesn't run into this issue.
In my case, I need a Desktop Power Automate flow to start after the computer restarts (from overnight updates) and autologin so there's no significant interruption in the flow that runs on a loop (with a pause of a few minutes every cycle).
PREVIOUS WORKFLOW
It was pretty easy to do by opening Desktop Power Automate and clicking the flow I want, three dot menu and "Create desktop shortcut". Then I would put that shortcut in the Windows 10 startup folder by going to Start menu, run, typing "shell:startup" enter and putting the shortcut in the folder. However after updating to the newest version, that's when I had the same problem. Even with toggling off the notification box. Then I followed obscure instructions to toggle the specific connector to be embedded from the cloud side of things, but no change.
NEW WORKFLOW
I created the desktop shortcut for the flow and left it on the desktop. Then I utilized AutoHotKey (version 2) to create a script with the below example code that would wait 140 seconds (shown in milliseconds) after reboot/sign-in, run the desktop flow shortcut, wait 10 seconds (giving enough time for the connector prompt to show), then trigger the "Enter" keyboard button to virtually press "Okay" to start the flow. Keeping in mind that I have the AutoHotKey file (.ahk) in the same startup folder listed above. It's not perfect but it seems to work.
Hopefully Microsoft makes it so we don't have to have another program running to run their automation program.
Here's the AutoHotKey (version 2) example code:
sleep 140000
run "C:\Users\youraccounthere\Desktop\NameOfFlow - Power Automate.url"
sleep 10000
Send('{Enter}')
