To run the spa in winter, all that has to happen is to put the automation in SPA mode. I went back and looked at your pictures before you took the plugs out and they put both return and suction actuators in open to both spa & pool then plugged the pool side so only flow would go to the spa side. They may have done this to facilitate blowing out the lines to the pool side. So with the plugs in place and the automated diverter valves open to both sides, it doesn’t matter if you are in Pool Mode or in Spa Mode because it will only draw water from the spa and return to the spa because the pool side is plugged off (disconnected). Furthermore they disconnected your automated diverter valves (remember when you found them unplugged) so that prevented anyone from moving between Pool and Spa mode.
As you can see, on the return side, flow can go both ways to the spa when the manual valve is open. That bypass valve would be useful if the spa was connected to the pool but it is not - so you need to keep that manual valve closed when in Pool Mode.
So in summary, now that all the pipes are connected - in Pool Mode, you must keep that manual valve closed on the return side as that allows pool water to flow to the spa. The best idea is to close the valve, then unscrew the thumbscrew on top of the handle, remove and store the handle and replace the thumbscrew so it is not loss. Therefore no one can turn that manual valve by mistake.
In Spa mode, all will work as planned.
So that brings up the question - how do you chlorinate your pool and spa? Since the 2 bodies are not connected, you need to test each separately and ensure that each are properly balanced.
Attached 2 pictures.
I circled in RED the 2 pipes you think are overflow pipes. You want to ensure these are open because if it rains, that is the only way it will naturally not overflow. The alternative is to drain the spa.

On the return plumbing, you can see when set in SPA mode, and you have the manual valve open, that water flow return to the spa can go both ways.
