
Russia’s Admiral Kuznetsov The Admiral Kuznetsov is not really a true carrier in a western sense and doesn’t have the same mission as a western carrier.
Moreover, she is classified as a heavy aviation cruiser for several reasons. (She carries offensive missiles not found on western carriers nor discussed during the Montreaux Convention)
Her sole mission role is fleet defense, although a previous foray into strike capability didn’t go too well in Syria and proved substantial limitations of the vessel.
The ski jump is adequate for the SU33 as mentioned, though they have to be loaded light.This is why she is not a strike carrier.
To be honest, the Russians would have been better off using the Mig 29K rather than the SU33 for her main air arm. As a result of the 29 being lighter and smaller yet still offering advanced capabilities like the bigger SU cousin. (Sukhoi 27 series and Mig 29 series have similar cockpits so pilots can transition easier almost like airbus philosophy)
The engineering gear has the same issues (and largely the same components) as the sovremenny destroyers.
Yes the whole power plant and engine components are Ukrainian — which is a big issue — but there is another massive issue you missed.
There is no dry dock able to accommodate her (the only one was the floating dry dock PD50 which sank), but the new dry docks being built in the north should come online in mid 2022.
She is a STOBAR carrier so the arresting gear is there. While there were some issues, it is ultimately effective.

The French had issues with the preceding Clemenceau class but that was resolved and the CDG uses an entire American system, although they use the 80m C13-3 compared to the 99m C13-1 that’s on the Americans (French cats are less powerful). Ultimately the cats both date back to the 1950’s British design on HMS Perseus.
Cross decking is not uncommon USN F18E have (very recently 2018 I believe) operated off the CDG and Rafael’s and Etendard off USN carriers over the years.It’s the same way with the UK except with harriers and F35B of the USMC.
As for the fuel well, it’s extremely low grade. It’s called mazut, basically unrefined waste oil that eventually clogs up the boilers and other components, effectively choking the system and giving you the black smoke.
The “Tug” is a supply ship similar to what the Europeans use for servicing Oil Rigs. It has the capability to do repairs and tow, and they primarily take the ship with them to address the lack of friendly ports and logistics.
Overall, though Kuznetsov is an embarrassment which I believe should be scrapped in favor of a better project, Russian gas turbines and Diesel engines are proving themselves in Russia and starting to be fitted to newer ships.
I will also add Lockheed bought Yakovlev and used some of the Yak 141 features in the F35B.
I got up close to the Yak 141 while I was in Moscow and many others in Monino.