As of 14.04.2020 There is an experimental feature in generally available VS Code to enable project wide problem reporting. Add the following to your settings.json:
"typescript.tsserver.experimental.enableProjectDiagnostics": true
It is still an experimental feature (after few years of neglect), so it can be both overwhelming and underwhelming at the same time. Good thing is that it apparently works with other languages as well and respects your config files.
Watch this space.