I don't know what the official definition is, but I'd consider deliberate mirroring of posture, online tone, and emotional state for conscious deceptive, and manipulative ends to be toxic empathy.
Trivial example - phone services with the stock "Your call is important to us but we're experiencing an unusually high level of calls right now" message. When the truth is the company is spending a bare minimum on phone support and knows it.
Or customer service scripts that say something like "I understand you're frustrated that you're having this problem."
In reality there's no understanding. And there may not even be any interest in fixing the problem - because when you read back through other messages you see the problem has been there for years and there's been absolutely no effort to find a fix.