GNU Global is a tagging system. There's no language service running in the background. You need to press F1 and execute Global: Rebuild Gtags Database to generate tag files before you can use other features.
Upon saving your code, this extension will try to update tags files incrementally by running 'global -u'. If the auto update didn't do well for you, you can manully run this command to rebuild all tag files.
You may want to add the tag files, which are GTAGS, GRTAGS, and GPATH, to your global gitignore setting.