I don’t believe this is possible, thus it’s a fixed 360°. I think limiting a “full” pan, like a “scan view area” thing could be useful. There’s a Wishlist topic requesting user-specified pan/tilt limits:
As with any Wishlist topic, you can visit that one to click or tap the Vote button above the initial post and share your ideas and use cases in the comments to show your support for the product and feature request/suggestions that are important to you.
I think user-defined limits would be especially useful for screening out static walls and other things most people probably would not want to see and made my own suggestion in that topic related to this.
It may not be clear even from the relevant Help Center article, but my understanding is that the 360 Scan control is for a one-time manual operation while viewing Solar Cam Pan’s Live Stream screen. You tap it and the Cam does a sweep before returning to its Home Waypoint. It’s not an on/off toggle feature, like the adjacent Track Person control. Note that it does not turn green when you tap it.