First, thank you! Sadly, this didn't help. In ended up deleting (renaming) ~/.config/Code which helped. Luckily enough all the plugins survived because they are installed under ~/.vscode

Actually, while figuring things out, I did also install Codium and copied the extensions folder from VSCode to the codium folder... Works like a charm - might stay there for the peace of mind.

I am on X11. rebooting, reinstalling and code --disable-gpu didn't help. Only deleting the config files. However, reading other comments it seems code --disable-gpu seems to work for most folks.