GNS 530 CDI output correct behavior?

Not necessarily directly related to MSFS, but the steam gauge 172 does have a GNS 530 which got me started down this rabbit hole, and in any case I haven’t found information anywhere else.
How does the GPS guidance output to an external CDI work on the GNS 530, and is the MSFS implementation correct? As far as I can tell, in MSFS at least, when the GNS 530 is in GPS mode and a flight plan with multiple waypoints is loaded, it automatically deflects the CDI needle to guide you onto the course path line drawn between the waypoint you last passed and the waypoint you’re heading towards (the purple line between the waypoints on the VFR map, in other words). The OBS knob has no effect on the course the CDI attempts to guide you to when you’re in GPS mode. But in actuality, I can’t tell if that’s the case at all. The GNS 530 manual itself doesn’t say anything about it, and I’ve yet to find any POHs for aircraft like the steam gauge 172 with a GNS 530 instead of some King GPS receiver or another. In an actual aircraft, do you have to turn the OBS knob to the course you want to fly to the GPS waypoint, like a radial on a VOR, or does the GNS 530 automatically deflect the needle to put you on that purple waypoint path? And for that matter, would, say, a KAP140 autopilot only link to the standalone CDI, navigating via the GNS 530 controlling that CDI, or can it get course information from the GNS 530 directly (via the GNS 530 essentially outputting CDI data to drive the autopilot onto either the purple GPS waypoint path or a VOR radial using its internal receiver and radial selector), making the whole course issue irrelevant?

You may not find a manual for it. I did a search for C172’s with that GNS package and there was only one real-world entry in all of the sim-related pages. That one was from a C172 board regarding an aftermarket mod.

The un-modded 530 OBS button has no effect, but the modded one does. It pauses the route, and allows you to choose the bearing you wish to approach the next waypoint.

So basically when the OBS button isn’t pressed it automatically calculates the bearing to approach from so that it lines up with the path between the waypoints, but when it is pressed you can dial in the approach bearing like a VOR?
If that’s the case, how does it output that to the external CDI? Does it override the OBS knob on the CDI to set the approach bearing to line up with the waypoint path?