Apple Diagnostics startup key D invokes Software Update over internet

Try the following: Reset NVRAM or PRAM on your Mac - Apple Support

Next, if necessary, boot into Safe Mode by booting with the Shift key held down and check there to see if the problem persists.  Then reboot normally and test Apple Diagnostics again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

If you give it time to attempt to connect and it never begins to boot to the online installer/diagnostic, then for some reason the Mac is not properly connecting to your local network or Internet using the Ethernet cable. I've sometimes had issues like this when repairing some of our organization's Macs. Many times I will boot back into macOS and double-check I have a valid IP address for the Ethernet connection, then I reboot and try to launch the online Diagnostics or Internet Recovery Mode which many times will just begin to work.

Try clicking the "...." and manually entering your WiFi's SSID and password in case the stored information is corrupt (the PRAM reset should have the default WiFi credentials removed unless of course you booted into macOS after the reset). Even if you select your SSID from the list you should be prompted for the WiFi password after the PRAM Reset.

There is no way to manually choose the Ethernet connection. The Mac will automatically use the Ethernet connection when it is present and should just beginning booting to the online diagnostic/server.

Does your Mac boot normally or into Safe Mode? A failing hard drive can interfere or even prevent the Mac from booting to external media including the online diagnostic or installer.

Geir Kristoffersen wrote:

Both Option d and d does in

OSX 10.15.7

All I get is a black screen with a globus and a drop down menu with the wireless networks in range.

This is normal since the online Apple Diagnostics leverages the online Internet Recovery feature. Select your WiFi network or if your WiFi network is not shown, then click on the "....." so you can manually enter the WiFi's SSID and password. Or connect the Mac directly to the router using an Ethernet cable.