I read this not necessarily as "Russian interest", but rather "limited Russian options", which they are completely correct about regarding the latter.
There are only so many countries capable of producing stealth fighters, and even fewer capable of producing navalized stealth fighters.
Should the Russian Navy christen a CV(N) as its flagship next decade, it'll be unsurprising if Russia finds itself in the same position with China as the UK and Italy, which operate the F-35B from their carriers, do now with the US.
The mention of "purchasable AWAC deck aircraft" is very interesting. Such lighthearted reference could indicate the KJ-600 has the potential for export, something we are not aware of.
The E-2 originated as a clean sheet AEW design for carrier operations, but with the exception of the US Navy and French Navy, all of its operators are land based. So in theory, there might be an export market for the KJ-600, but in practice not quite.
The US has or more precisely had nothing sitting in between the E-2 and E-3, but China does, and an export derivative of the KJ-700 shouldn't be much more expensive than the KJ-600.
So unless Russia, Brazil, Argentina, Saudi Arabia or some other country with potential CV(N) ambitions decide to import the J-35 naval fighter for carrier operations, it's unlikely the KJ-600 will be exported.
Russia building a new aircraft carrier for distant power projection just isn't credible.
They'll have to focus on a potential European land war, against a much larger NATO as the adversary.
So that means the Army and Air Force take priority.
Inclined to agree with you that Russia needs to prioritize their army and aerospace forces over their navy, but also wouldn't discount what Ilya Kramnik told Izvestia.
He is tied to the Russian analogues of CFR, Brookings, RAND, etc., which means his takes
may be informed by considerations that are largely underreported or effectively unknown outside of Russian national security and foreign policy circles. In short, it's tough to outright reject his views when he knows things we don't.
Alternatively, someone can always shoot him an email to see if he'll elaborate on the likelihood of the J-35 entering Russian service.
Though we probably should also acknowledge that the publicized views of such SMEs are at times tainted by political considerations, especially due to competition within state and state adjacent apparatuses.