Actual free synergy upgrades have no GS charge, you’re likely referring to converting synergy from max leveled ships to free synergy, which means you likely ran out of it, if you want to earn free synergy faster you could use a premium ship, 20% of the synergy they earn is free synergy compared to a regular ship which only earns 5%.
If you still have questions about the game consider messaging players like me instead of making a thread for every one of them, makes moderator’s jobs easier.