Spying
Instead of spies, it helps to think of your agents more as hackers, because that is what they really are. They are agents your government sponsors that try to steal technology 'over the wire'. Everything they do is done by computers.
The things they can do are:
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Hide - They will crack someone's name/password in the enemy empire and just use that information to look around inside their systems and get a general idea of what is going on. They won't attempt to do anything that might get them caught. As long as they don't they are unlikely to actually get caught.
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Sabotage - They will try to gain access to the remote mainframes of enemy factories and defensive locations and they will try to hit the 'self destruct' button remotely across the galactic internet. Sometimes they will succeed and the results will be the complete destruction of some of the enemy's facilities. By doing this, they are very much more likely to be caught and to have their access removed, ending the spy's access to the enemy's network.
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Espionage - They will try to hack into the enemy's research network and download the schematics for the enemy's technological advancements. The enemy has different research networks for each research type, and they don't have much time once they get in so you have to make a split second call about which research network to infiltrate and the hacker will just try to take anything they can get their hands on as part of that network. They will always get something you don't have, but there is no telling what that will be until the schematic is analyzed on the inside. Essentially, you show them blueprints of what technologies not to get, and they just get the first thing they see that is completely unlike that stuff you showed them. If even they do this, it is highly likely that they will get caught and have their access removed.