Sate Affairs/Secrets override the 1A because the fate of the country may be in the balance, so I do understand that need. I mean this is state-state business and communication, not Jack and Joe Nobody.
It is not state-state business and communication. That kind of thing is not done on Twitter. At all.
The closest is propagandistic back and forth needling, but that's not diplomacy, it's PR/propaganda: the real audience for that is the public, not the other state's government.
Even when two states lack official diplomatic relations, they don't resort to Twitter. There are other mechanisms for that (e.g. https://en.wikipedia.org/wiki/Protecting_power and agreements brokered through other 3rd party diplomats like http://www.parstimes.com/history/algiers_accords.pdf).