Good, interesting find. Here is what I think:
Jhanas are not just a list of four separate states, they are a progression of the same principle developing and getting stronger from one phase to another.
The principle is that as our skill (of seeing and overcoming obstacles to peace, which is what meditation, and indeed the entire Buddhist path, is about) increases, we overcome subtler-and-subtler types of obstacles and as a result our happiness gets subtler-and-subtler, too:
- In the beginning we generate crude happiness by "detaching" ourselves from unwholesome experiences and ideas, and by remembering and going over certain wholesome ideas that elate our mind.
- Then we "detach" from this crutch of the wholesome ideas that we used on the previous step, and master a non-discursive method of generating happiness (of subtler nature) by focusing on the (psychosomatic) experience of inner unity, inner confidence, being at peace and comfortable in our own skin.
- Then (and this is what's called the third jhana) we "detach" from any notion of spiritual goal or success, including the very notion of inner harmony that we cultivated on the previous step. Now we dwell in effortless peace, without any sense of "practice" or "cultivation".
- Finally, we "detach" from any judgement or comparison that we used to apply in order to categorize our inner state as "peaceful" vs "disturbed".
As you can see, on every step we overcome the limits inherent in valid practice of the previous step, expanding our mind to include what we previously left out, and reducing the tension that comes from division.
I believe the word you found in this version of agama sutra, 空, is there to emphasize the sense of effortlessness and goal-less-ness, the peaceful exhaustion of striving that is characteristic of the third jhana.
This all-encompassing effortlessness is illustrated by the image of the lotus pond used in the Pali Suttas:
Just as in a lotus pond there may be some lotuses which, born and grown under water, stay immersed at all times, never sticking out of the water.
These lotuses don't need to try and immerse themselves in the water. Water is already all around them at all times. The same way, a meditator who has mastered the third jhana has mastered dwelling in effortless peace. Because they let go of any sense of striving for a goal, including the spiritual goal of enlightenment or successful meditation or anything like that, they never "stick out of peace" no matter where they go or what they do. It's like being in retirement, there is nowhere to rush and nothing to worry about.
This sense of effortlessness, goal-less-ness, purpose-less-ness, vacancy - is what's meant here by the word 空.