In UEFI settings menu, choose Exit Setup, and you should see the following screen:
Can you post a screen shot of yours?
You SHOULD be able to get a recovery image with Windows 10 for your SP3. It will be older, but you can then update to the latest version. Go to https://support.microsoft.com/en-us/surfacerecoveryimage
(with a different Windows computer if yours is not working properly)
and download a recovery image for your Surface. You will need a 16GB or 32GB USB stick (also called a flash drive) formatted FAT32 (use a Windows computer). You can't use an actual external USB hard drive for this. Best to purchase and use a new, previously unused USB stick for this. Use FULL format and not quick format and give the volume a name like surfboot. Unzip/extract the recovery zip to the root of the formatted USB stick and then:
To reset your Surface from a USB recovery drive:
Step 1: Make sure your Surface is turned off and plugged in (hold down the power button for 30 seconds).
Step 2: Insert the USB recovery drive into the USB port on your Surface.
Step 3: Press and hold the volume-down button while you press and release the power button on your Surface.
Step 4: When the Surface logo appears, release the volume button.
Step 5: When prompted, select the language and keyboard layout you want.
Step 6: Select Troubleshoot > Reset your PC.
*If prompted for a recovery key, select Skip this drive at the bottom of the screen*.
Step 7: Select the target operating system you wish to reset. This refers to the current operating system installed on your Surface.
Step 8: Select Yes, repartition the drives, and on the next page, select Next.
Step 9: Choose Just remove my files.
Step 10: Select Reset.
Surface restarts and the Surface logo displays while the reset process continues (this can take a while).
When completed, go to Download Windows 10 (microsoft.com) and select Update Now.