Gaming services installation failure is relative straightforward now:
Close the Xbox app (not minimised in taskbar)
Open up the Powershell in Admin mode and type in the three lines:
Get-AppxPackage *gamingservices* -allusers | remove-appxpackage -allusers <Enter>
Remove-Item -Path "HKLM:\System\CurrentControlSet\Services\GamingServices" -recurse <Enter>
Remove-Item -Path "HKLM:\System\CurrentControlSet\Services\GamingServicesNet" -recurse <Enter>
Reboot pc.
Reinstall gaming services via the powershell:
start ms-windows-store://pdp/?productid=9MWPM2CQNLHN
I'd even go to say this may not even be needed. For a while now purely having the xbox app completely closed, any gaming services error i've gotten rights itself after a retry.
Regarding the "Something happened at our end..." error, I haven't worked out the cause for this one yet. I'm sure it won't require going so low as require a OS reinstall. I never go that far.