What you are describing is not a normal “select Recovery Mode” situation.
The key point is:
Start → Microsoft logo → Boot Select
Recovery Mode → Microsoft logo → Boot Select
Android Recovery never appears
If Recovery Mode itself cannot load, the normal adb sideload recovery procedure cannot be performed. This could be corrupted boot/recovery data or a problem with the internal storage; the loop alone does not prove a hardware failure.
Before doing anything destructive
If you have important data on the Duo, do not factory-reset, erase, or manually flash partitions yet.
Install Google's Android Platform Tools, connect the Duo while it is at Boot Select, and run:
fastboot devices
If it is detected, you can also run:
fastboot getvar all
These are diagnostic commands only. Remove the serial number or other identifiers before posting the output publicly.
I would not recommend blindly running commands such as fastboot flash boot or fastboot flash recovery. The correct Surface Duo partition layout and Microsoft-provided recovery procedure should be followed; guessing at partition names/images can make recovery more difficult.
If Fastboot does not detect the Duo, or the commands fail/hang, stop there.
Microsoft Support
When contacting Microsoft, don't simply report “Duo won't boot.” Tell them:
Surface Duo is stuck at Boot Select. Start → Microsoft logo → Boot Select. Recovery Mode → Microsoft logo → Boot Select. Android Recovery never appears. Bootloader Version: 2022.815.527.
Also provide the result of fastboot devices.
Given that Recovery Mode itself is failing to load, it is reasonable to ask Microsoft for a service/replacement assessment rather than being directed repeatedly to select Recovery Mode.
If the device contains important data, explicitly tell Microsoft not to perform a factory reset without your authorization.