Can you try disabling Hardware Acceleration in settings to see if this resolves the issue?
You’ll find this in Settings --> Additional Settings --> System --> Hardware Acceleration
If Brave shuts down to quickly, open Command Prompt and then enter this command: "C:\Program Files (x86)\BraveSoftware\Brave-Browser\Application\brave.exe" --disable-gpu
Do you know if you’ve enabled Sync via brave://flags?