I think others have encountered this before, and I also seem to be persistently unable to have an auto-update succeed on my Windows 10 Surface Book 3. This has happened to me for the last 4-5 updates I’ve been advised about.
The Windows 10 client app notifies me of an available update, prompting me to restart. I confirm, it seems to uninstall the current client, but upon completion when I tick the box to re-open Bitwarden, I get a Windows message about a missing shortcut and there’s no sign of the new version. If I go to bitwarden.com then download and install the latest version Windows installer (Bitwarden-Installer-1.23.0.exe as I write this), it seems to work OK.
I can probably persevere with this, but it seems to be a persistent problem and I thought it’s better for the user community to solve it so we don’t deter others exploring Bitwarden as an option.