Be careful folks! rust-analyzer is currently (accidentally) breaking VSCode extension updates.
Here's the issue: https://github.com/microsoft/vscode/issues/149518
Basically, if you have rust-analyzer installed, you won't get any VSCode extension updates, which could be a security concern. I was able to uninstall rust-analyzer, update all my extensions, and then re-install it.
Please let's be kind to both VSCode and Rust, software is hard and sometimes mistakes get made. Props to both communities for already figuring out what's wrong, and having plans to solve it.