Is "Moving at the speed of light into eternity" a hyperbole? If not, what is it?
It might be an analogy
At the speed of light time ceases to exist. So at the speed of light an non material consciousness has entered eternity as time is now infinite. The past present and future are all one at the speed of light.
A person can not actually achieve the speed of light but an idea could be considered to have spread so fast that the idea has now become eternal.
If in reference to a material person or object it would have to be hyperbole.
The reference does assume some understanding of relativity and physics which is possibly not a good assumption as this is not common knowledge.