The latest version of Visual Studio Code (1.86.0) released in January 2024 requires a later version of GLIBC than is currently available on the NeSI login nodes.
For the moment please roll back to the previous release (1.8.5).
You will also have to roll back the 'Remote - SSH' plugin. This can be done by selecting the plugin in the Extension Marketplace, clicking on the 'Uninstall' drop down and choosing 'Install another version'.
Due to the amount of feedback on the glibc change the VSCode team have said that future versions will allow you to connect with a warning instead.
You can get the fix in a pre-release build (1.86.1), or wait for the next stable release in March.