Compassion can indeed be taxing because it often motivates us to want to rescue others. Compassion seems to inspire the image of the Atlas that has the world on his shoulders. That’s not very sustainable. I’m sure you’ve heard how care givers often burn out.
Empathy, on the other hand, is about creating connection without judgment. No judgment of good or bad and right or wrong, for example. This means nobody is trying to rescue anyone. It is about remaining in a creative state. Sometimes this comes naturally. Others times this doesn’t come naturally. For us to realize empathy in situations where this doesn’t come naturally we often need the support of others. Otherwise we can get stuck in a rut having difficulty empathizing. (i.e kinda like waiting alone for creative inspiration to strike vs brain storming with others for the creative inspiration) So to get unstuck, a provision of an effective support system is critical. That support system can make empathy quite a bit more sustainable.