I hereby invent a new acronym: ASF, for Anti-Structure Frigate!
Impressions so far with ASFs:
They have fairly bad behavior when put in a fleet. For example, if a fleet is bombing an enemy planet and there's nothing left in the gravity well but extractors and logistics structures, the ASFs hang out doing nothing rather than attacking the structures.
Also, ASFs should probably come out of the factory with fleet auto-joining turned on.
They don't do well with auto-targeting during combat, either. If ASFs are in a fleet attacking a starbase, they may use their attack abilites to nail unarmed orbital structures if those structures are closer to the ASFs than the starbase.
The frigates should learn how to prioritize targets, and also how to stick with them. The Advent frigate has a long cool down, and if left alone after using its ability, the ship gets bored and automatically returns to its previous position or reforms with the fleet. Then, 20 seconds later, the cooldown ends and it makes a U-turn to attack the same target - but it takes 20 seconds to move back to attack position.
There's also inconvenient behavior when giving orders to a group of ASFs. If you select 8 ASFs and right-click on a starbase, the frigate that's selected "on top" will take an order to use its attack ability - but the other 7 are issued a move command. The only way to make a group of ASFs focus fire is to individually select each one and give the orders separately.
But, although currently inconvenient to use and order around, ASFs are quite effective against structures. A few of them can rapidly wipe out normal structures, and a large group can effectively take down a starbase. It's worth bringing a few along if your opponent is using the new defensive structures and starbases.
The only thing I've noticed is that ASFs have fairly long build times compared to what I'd expect. Given that they're inflexible, middle-tech-tier units, the time required feels relatively long.