Error while updating to version 1.0.5683: Download fails

[BalduinLandolt]

Describe what happened:

VS Code indicates there is an extension ready for updating. Under the Live Share extension there is a button "Update to 1.0.5683".
When I click it, a prompt shows up: "Error while updating 'Live Share' extension. Please check the log for more details."

the logs say:

[2022-08-09 14:18:58.314] [renderer1] [error] ["Download: XHR failed","    at Q.downloadExtension (vscode-file://vscode-app/Applications/Visual%20Studio%20Code.app/Contents/Resources/app/out/vs/code/electron-browser/sharedProcess/sharedProcessMain.js:83:169038)","    at async Q.doRun (vscode-file://vscode-app/Applications/Visual%20Studio%20Code.app/Contents/Resources/app/out/vs/code/electron-browser/sharedProcess/sharedProcessMain.js:83:168169)"]
[2022-08-09 14:18:58.344] [renderer1] [error] XHR failed: Download: XHR failed
    at Q.downloadExtension (vscode-file://vscode-app/Applications/Visual%20Studio%20Code.app/Contents/Resources/app/out/vs/code/electron-browser/sharedProcess/sharedProcessMain.js:83:169038)
    at async Q.doRun (vscode-file://vscode-app/Applications/Visual%20Studio%20Code.app/Contents/Resources/app/out/vs/code/electron-browser/sharedProcess/sharedProcessMain.js:83:168169)

What was your system configuration? Product and Version [VS/VSCode]: VS Code 1.70.0 OS Version[macOS/Windows]: macOS Live Share Extension Version: v1.0.5679 Target Platform or Language [e.g. Node.js]: n/a

Steps to Reproduce / Scenario:

1. Try to update the extension

Please attach logs to this issue:

logs.zip