This is by design and is because you installed Visual Studio Code per user rather than per system:
VS Code provides both Windows user and system level setups.
The user setup does not require Administrator privileges to run as the location will be under your user Local AppData (LOCALAPPDATA) folder. Since it requires no elevation, the user setup is able to provide a smoother background update experience. This is the preferred way to install VS Code on Windows.
Note: When running VS Code as Administrator in a user setup installation, updates will be disabled.
Contrary to popular belief, Windows programs installed per user don't actually need administrator rights to run or update or install, because users have read/write permissions to their own drives/folders by default. Only programs installed for all users require a user to have local administrator permissions (to install in Program Files, for example).
So to resolve your problem, stop running this user-specific installation of VS Code as an administrator, or uninstall it and use the system installer of VS Code to install it for all users, instead.
For user-specific installations, you don't need to run 'check for updates' manually, because VS Code will check and install them automatically in the background, as the quote above indicates.
Answer from TylerH on Stack OverflowCheck for Updates missing since Insiders 1.70.0
Check For Updates button is missing
Check for Update Missing
Check For Updates menu option missing
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Hello there vscode subreddit, this is my first time being here, so sorry if I read the tone of the sub wrong (a place for VScode help and jokes). Some context is required for my issue. First of all, this is on a school computer, so some things I can't do, like using admin privileges, command prompt, and even task manager. VScode is on a specific list of apps that can be downloaded from the Software Center, so it is allowed to be on my computer. (I don't want to get in trouble with the district, lol) This version, however, is an outdated version of VScode that does not support some of the extensions I would like to use. When I click "check for updates" in the help menu, it changes into an "install update" option. When I click on that, however, the program never gives me any prompts or any indication that it is downloading the update other than the clock in the bottom left and the grayed-out option in the menu. Any tips on how to make it update?
Running this from the command prompt seemed to work for me: ( close all vscode windows first )
winget upgrade --id Microsoft.VisualStudioCode
I think because I was running vscode as administrator I did not see the Help->Check for updates menu item.
If Update:Mode in VS Code's setting is on 'none' , 'Check for Updates ...' option will disappear from Help. Just be sure it's not on 'none' then you can check for updates.