Let's look at the long term here. Korinthos are unlikely to even be able to hold Kerkyra against Athens. Historically, Athens smashed them.
If they do manage to hold on, they will not be able to hold it
long, and just trying to do so against Athenian interference will give them far too much to worry about than picking a fight with us, a near-peer naval power. It makes no sense from their perspective.
Korinthos also can't "cut off" the Adriatic by holding Kerkyra, because that is not how naval power
works in this century, or this
millennium for that matter. Just to clear that up.
Our best bet for an Adriatic Empire is to let them bleed themselves in games like this whilst strengthening and securing our position at home, perhaps establishing a few more trade colonies or doing an anti-piracy operation, and then, when we are
ready, sweeping in and smashing them in a decisive naval battle, if we even
need to. Which we may not by that point. Kerkya is essentially a distraction that will weaken us before we are ready.
In the unlikely scenario that it does become a problem, we can move to intervene supported by our Italiote neighbours. Because they have an interest too here in other powers playing games in Italy, let's remember.
Acting unilaterally and too early here would be a real blunder.