Cursor was based on quite an old version of VS Code laat time I checked, so it's possible Microsoft just didn't target compatibility with a release from six months ago.

This is also what's said here by one of the devs: https://github.com/microsoft/vscode-pgsql/issues/15

Looks like manually loading the VSIX to bypass the compatibility check should work but who knows how stable that'll be.

You can download the .vsix file directly from marketplace.visualstudio and install it in cursor.