Russia is not happy about having THAAD in Poland,

THAAD isn't in Poland

why would they be happy about having it deployed in their backyard, in South Korea?

South Korea is a sovereign country, not a "backyard of Russia".

Russia considers THAAD a strategically offensive weapon.

No, they don't. They have come up with some wild fantasy scenarios that THAAD can be fitted with ground attack missiles, but in reality, they only care about THAAD becuase of the powerful TPY-2 radar, which doesn't pose an existential/MAD-destabilizing threat to Russian forces in the Far East Military District.

They're primary angle in deescalation on the peninsula is getting THAAD deployment rescinded.

Their primary angle in the peninsula is using NK as a wedge to build up influence (or the domestic+international perception of influence) against the US and Japan while maintaining their healthy trade relationship with South Korea. If they can get rid of the TPY-2 radars, it doesn't really matter because those are already stationed in Japan.

Having a missile defense shield in the Pacific seriously destabilizes MAD far more than a nuclear-armed Korea.

No it doesn't, because THAAD is only for the terminal phase of up-to IRBM class missiles, not ICBMs which aren't even deployed in the region. Unless Russia is planning to nuke South Korea with Iskanders, this does absolutely nothing outside of providing an extra TPY-2 radar in the region. There is no element of a missile shield in the Pacific that can feasibly shoot down Russian ICBMs except GMD in Alaska, which only has enough interceptors to handle one-off threats like a few North Korean missiles.

THAAD is more relevant to Chinese military balance, Russia is only using this as a rhetorical sticking point to shore itself up as an ideological+practical geopolitical haven for countries outside the US hegemony.