I wonder what the reasons were for the Su-33 escorting the Tu-160?One aspect of the recent deployment observed was the use of Tu-160s for long range strike, and the Su-33 force able to provide close fighter support to those bombers at the point of attack. Due to the reach of the Russian naval aviation forces, I suspect Russia sees tremendous value in protecting its bomber force with forward deployed carrier based fighters, particularly in a land attack mission profiles against a lesser power.
From a strategic perspective, long range bomber sorties from Russia guarded at the point of attack by forward deployed CV aviation is an enormous capability, a capability beyond any nation in the world besides the United States. In my opinion, that advantage is hardly "less relevant in the current strategic environment", I see it as just the opposite given the difficulty of forward basing for Russia.
Could it be to develop interoperability capability? Is Russia concerned with the low number of Tu-160s in their inventory?
I feel it would be more difficult to defend a CVBG against just Tu-160s sneaking in, than Tu-160s with a Su-33 escort. Having the Su-33 operating anywhere is a tip off that Kusnetsov CV is in proximity which will raise the awareness level of a USN CVBG putting up an a more robust fleet air defense. The Kusnetsov with her SS-N-19 ASCMs will also surely call attention.
You will probably have DS SSN protecting the CVBG from SSGNs and a SSN shadowing the Kusnetsov.