Dogfights in the post Top Gun era?

Didn’t even need to fully sink it. Just make it incapable of flight operations.

Yup. Admittedly American and British carriers in WW2 illustrated the ability to often stay in the fight despite absorbing multiple hits. Maybe modern carriers might not?
The loss of the Moskova is food for thought though.

The antagonist aircraft in Top Gun are not explicitly identified, but they were North Korean in the original script. The markings on the tail in the actual film are consistent with Chinese PLAAF markings.