Different Google Drive icon in sidebar?
Sadly, this is simply not possible in macOS. The Google Drive app, and now its successor Backup and Sync from Google, give the actual folder named "Google Drive" its custom icon in the conventional way, much the same way you could paste a custom icon on any other folder.

Unfortunately, all custom folder icons are ignored when displayed as Favorites in the Finder sidebar. You can confirm this by adding any folder with a custom icon to the sidebar. You can also show your home in List view to see that "Google Drive" does indeed have a custom icon optimized for that tiny display size. Finder is simply designed to ignore it, presumably to keep the Finder user interface as uniform as possible.