Embassies (or technically chanceries, as embassies are the staff) are technically still territory of Ukraine, although if any German staff were killed or if Germany was the target that would be grounds for a declaration of war
The MAD doctrine (Mutually Assured Destruction) is from the Cold War and essentially states no one will use nukes in a war because both sides know they will both be completely destroyed in a nuclear war
That being said Putin would totally be the kind of guy to ignore that