There are two kinds of ships:
SUBMARINES...........and...............TARGETS.
Take it to the bank.
An aircraft carrier is a.... big.... fat....TARGET!!
That assumes a carrier sails someplace alone. It doesn’t as you well know. It has its own concentric rings of submarines, cruisers, destroyers, as well as ASW aircraft. Let’s not forget sonar, and other counter measures.
A carrier battle group is nothing to toy with, even if you are a very sophisticated Russian boat, diesel or otherwise.