Russia has the capability of causing a lot of trouble without getting into aerial wars
That is correct. But still not a match for NATO or even the US alone for that matter. Remember, the US indirectly defeated the Soviet army (which was numerically stronger than current Russian army) in Afghanistan by providing light and medium weapons to ground based insurgents (and these insurgents eventually ended up attacking the US). In simplest of terms, the US has a lot more money to spend on proxies vs. Russia.
such a huge gap?
In terms of ultimate mechanical and aerodynamic performance not so much, but F22 was designed from concept to completion with stealth capabilities while the SU27-30-33-35 family was not, and the F22 has significantly
better electronic warfare capabilities, and this is why (in my opinion) it would win in real world battles. It essentially thinks faster, therefore allowing the pilot to take action MUCH faster, often before its opponents have even achieved situational awareness.
4 x F22 practically means the Russians could lose entire small sorties of their most capable fighters with zero or near-zero loss to NATO.
If the Russians throw in 50 x MiG29 then they CAN create a lot of aerial trouble, but they are likely to lose planes at a ratio of 10:1 against NATO specifically because of the electronic warfare superiority mentioned earlier.