In the statement of purpose, I have research work that's in progress and will be part of a manuscript to be submitted likely after applications season. How should I go about describing my current research and future research goals? I feel I would necessarily have to go into some details about my work with our research group, but I wonder if there is then a risk of getting ideas scooped by the admissions committees.
First, as Caharpuka says, make sure to discuss this with your supervisor / PI and any other collaborators who are involved in your research. Ask them about how much detail they are comfortable with sharing, and show them a draft of your statement before submitting it.
However, in general, you want to give enough details so that it is clear what you are working on. You want to show that you have a deep understanding of the overall project as well as your specific tasks.
It is pretty unlikely that an admissions committee member would try to scoop you. First, it's generally agreed that student / job / grant applications are confidential, and it would be highly unethical for a committee member to use such information for their own benefit. Second, researchers usually don't lack for ideas of what to work on, so they don't need to steal them; usually the limiting factor is the time and resources to work on the ideas they have already.
So, err to the side of more details. The risk is small, and it is far outweighted by the benefits.