I noticed that when I use "Check for Updates..." on ARM64 Windows (Surface Pro X), using VS Code Insiders 1.64.0, it appears to download something then pops up an error message with:

Perhaps there was a publishing issue causing the wrong architecture to be associated.

Version: 1.64.0-insider (user setup)
Commit: c6e58d1
Date: 2022-01-14T05:19:33.429Z
Electron: 13.5.2
Chromium: 91.0.4472.164
Node.js: 14.16.0
V8: 9.1.269.39-electron.0
OS: Windows_NT x64 10.0.22000