In a spin, are both wings stalled?
Yes, both are stalled.

I guess a nit-pick is on "what is stalled"? I adopt that you are at or beyond the point that an increase in AOA results in an increase in lift (critical AOA). That's the top of the blue curve in the plot below.

Also, a stalled wing does not mean every point on the wing has unattached flow. It means the wing is operating at an AOA where an increase in AOA results in a decrease in lift.

At low angles of attack (AOA) planes are naturally stable in roll. The downgoing wing sees a higher AOA which results in more lift, and a restoring force. The upgoing wings sees a lower AOA, and less lift, so it is stabilizing too.

At a high AOA, though, you are operating on the backside of the wing lift diagram. In the picture below, this would be at and beyond 20 degrees AOA.



Now, the upgoing wing sees more lift, which leads to positively reinforcing going up. Same but opposite on the downgoing. It sees less lift.

Also, the red line shows drag. That downgoing wing (on inside of the spin) sees a great increase in drag, which will lead to a yaw towards that wing, i.e., pro-spin.

So to get in the situation where a roll/yaw movement is positively reinforcing, you need to be in stalled AOA. You might start with just one wing, you'll get to both.

JMHO!

EDIT

Here’s a NASA video of a wing with tufts when it is both on the inside of the spin and outside. Stalled in both (but different airflow).