Hi benoitvm,
Thank you for reaching Microsoft Community and I'm sorry to hear about the issue you are having the device performance.
May I know how did you try stopping the Windows Update service? Was it through the Services app?
Please open Device Manager, expand Firmware and double-click Surface System Aggregator. Go to its Driver tab and share us with the Driver version installed.
Please try running these steps also on your Surface Pro 7 for now:
1: Run Surface Diagnostic Toolkit
See: Fix common Surface problems using the Surface Diagnostic Toolkit (microsoft.com)
2: Update drivers and firmware
Check what is the current OS Build of your Windows version by going to Settings > System > About.
Go to Download driver and firmware for Surface, choose Surface Pro
Then click the link next to Surface Pro 7 then click Download on the next page.
Choose the .msi file that matches your current OS Build and click Next.
After downloading, run and install the .msi then Restart.
Hope this helps.