This is a rather old topic, but it could still be informative. How ever; when I search on “How open an exiting Workspace in PlatformIO/VSCode” I don’t find what I, looking for.
What I do find is this:
pfeerick says:
“Workspace - VSCode allows you have multiple projects within the one workspace, which can be saved and re-opened later.”
Quite nice, that’s exactly what I have, but…
How do I open that existing Workspace with all my projects and their dependencies in it?
Same issue. It’s not right now evident how to do that.
Did you find an answer pleas update you question… 
Pressing the “House” icon in the toolbar brings up the PlatformIO “Home” which has a button “Open Project” opening a file-browser.
Just browse to the folder containing “platformio.ini” and select open.
Why it did not do that first time…?
Clarification: you open a folder (a single project) that way. A workspace is a collection of projects, it is created when you open multiple folders at once. It can be saved as a special workspace file to save you the hassle of reopening all folders the next time.