As the title says, I have managed to get Battlestations: Pacific to work on Windows 11 by following these steps:

1) Install Battlestations: Pacific from Steam.
2) Download Games for Windows Live and additional dependencies from the following link: https://community.pcgamingwiki.com/files/file/1012-microsoft-games-for-windows-live/ (Mr. Garrett was kind enough to include everything you need in one ZIP file.)
3) Install the .exe file and all the .msi files from the ZIP archive.
4) Log into the Xbox app on your Windows 11 using your Microsoft account.
5) Launch Battlestations: Pacific. On the loading screen for Games for Windows Live, log in with the same Microsoft account you used for the Xbox app.
6) After logging in successfully, wait a few minutes. It might take up to 10 minutes to finish setting everything up.

After setup, you should be able to play the singleplayer campaign, and your progress will be saved. There's a good chance multiplayer might work as well, but I haven't tested it yet. :)