For future reference you might try posting this in the appropriate sub forum:
https://www.gog.com/forum/star_wars_galactic_battlegrounds_saga#1494607689

HOWEVER, since I'm here and have played that mission a gazillion times, do you have enough resources? That mission starts you off with just enough iron and carbon to build a tower or two at which point you'll need to harvest carbon and trade for iron since you can't mine any until you hit their southeast islands.

Also, where exactly are you trying to build it. That patch where their dock was is very picky about placement and you will need a tower or two up before you even start building or their navy will literally blow the site to pieces the second you order it built. And by towers that includes missiles. Their air force will take you apart if their navy can't.

I've noticed the same issue. I've just launched the original game (without the clone wars expansion) and building shipyard works in this mission. (to easily launch the mission without the clone wars, as it doesn't use the same save, use the skywalker cheat code on the previous missions)