In Studio you could open a class directly via it's name, without having to traverse the package tree with multiple clicks until arriving at the desired class.

You would Ctrl + O or (File -> Open) and be able to simply type in the class name, for example:

You press Enter, and viola - the class is opened.

How do you achieve this in VSCode?

It's quite easy actually, you can simply press Ctrl + T (in Windows for example), or Go -> Go to Symbol in Workspace..., type in the class name and there you go.

For example:

This solution was mentioned by @Dmitry Maslennikov as a suggestion for the GitHub issue report (designated as an enhancement request) for this kind of functionality - "Open Class by Name from Server".

Here's a short GIF demonstrating this: