Cross-progression is available with The Division 2 for PC and Stadia.
If you own the Warlords of New York Expansion on PC, but not on Stadia you will only be able to access the expansion content on PC.
You will not be able to access your character on Stadia once you have started with the expansion, unless you purchase Warlords of New York for both platforms.
To take advantage of the feature, you will need to link your Stadia account to your Ubisoft account.
Please note that although you do not need to own the game on both platforms for cross-play, it is necessary for cross-progression.
If you own the Warlords of New York Expansion on PC, but not on Stadia you will only be able to access the expansion content on PC.
You will not be able to access your character on Stadia once you have started with the expansion, unless you purchase Warlords of New York for both platforms.
Let us know if you have any other questions.