Based on my knowledge, this sounds like another software interference issue that can affect Spine on startup. While I don't have specific information about Google Drive for Desktop causing conflicts, similar sync and cloud storage applications have been known to interfere with Spine's startup process.
Here are some steps you can try:
Temporarily disable Google Drive for Desktop during Spine startup - As you've discovered, quitting Google Drive allows Spine to launch. You might want to make this part of your workflow until a better solution is found.
Check for antivirus or other interfering software - Antivirus software is a common cause of Spine startup issues. Make sure your antivirus isn't scanning Spine files or blocking its processes during startup.
Reset Spine's user files - Delete your Spine user files to reset settings to their defaults. You can find information about user file locations at: https://esotericsoftware.com/spine-troubleshooting#User-files
Check your spine.log file - This might provide clues about what's happening. The log file is located at <user home folder>\Spine\spine.log (Windows) or ~/Library/Application Support/Spine/spine.log (Mac).
Regarding your question about ports - Spine does need internet connectivity for initial activation and version downloads, but shouldn't have ongoing port conflicts with Google Drive. The issue is more likely related to file system monitoring or sync operations interfering with Spine's startup process, similar to how other "Finder enhancements" and sync software have caused problems in the past.
If the problem persists, you might want to post on the Spine forum at https://esotericsoftware.com/forum with your spine.log file for more specific help.