From what I can tell of the design of this thing, it won't really do in-shore bombardment, either. It's got a couple of 5" guns, and some 30mm cannons. And neither of those are capable of over-the-horizon fire. The rail gun is a nifty idea, but they haven't been able to make it reliable and deployable. Not that they can't, of course. But we know what happens when you design-in something that doesn't work consistently (e.g. the main gun on the Zumwalt).

That’s what the rail gun is for: the Navy’s early tests were able to hurl projectiles as far as 200nm(!) away. That’s medium-range missile distance at a fraction of the weight, space and complexity of missiles. At only ~40lbs a shot, and at 6 shots/minute, it’s a ton of down range firepower:

usni.org - Naval rail guns are revolutionary

To put things in perspective, our current 5-inch gun has a muzzle energy of 10 megajoules (MJ). ERGM will increase this to 18 MJ, and AGS will press the limits of conventional gun physics by attempting to achieve a muzzle energy in excess of 33 MJ. In contrast, naval rail guns will achieve muzzle energies from 60 to 300 MJ.

Speed kills, as they say.
The Zumwalt designs didn’t go forward because of problems with replacing the barrels. But the Japanese have made some breakthroughs:

19fortyfive.com - Stunning japan railgun breakthrough has the u s navy asking tough questions

Japan Has a Railgun
Japan’s efforts to build and develop an electromagnetic railgun, a futuristic weapon that fires projectiles using electricity, appear to have been successful.

The Japan Maritime Self-Defense Force (JMSDF) released an image of its state-of-the-art railgun on April 18. It is currently undergoing testing aboard the test ship JS Asuka.

Other points:
-they seem to have solved the barrel problem, and got 120+ shots out of theirs.
-they hit a target ship with it
-they only spent like $6.5 million on the program!

The breakthrough:
Copper was initially used as the barrel rail material, but it was later changed to a different blend of metals and other materials during the research. As a result, it was confirmed that no significant damage occurred to the barrel rail even after 120 rounds were fired.

For the frigate:
Coast Guard duties often differ from Navy duties, so it would be surprising if those ships don't need some serious mods to take on the latter. Coast Guard can do (and has done in the past) combat, but that's not really what they're equipped for.

The main differences are going to be in electronics.