Waterbear, first I want to thank you for your help and the attention you're giving to my issue.
I'll clarify one thing that I did by way of typo in my FWIW remark. I meant to say IF ieave the spa drain valve open when the pool is off, the spa drains into the pool. That is not my practice. It was simply a way to check whether the valve was actually opening the spa drain. It does. If the pump is off, and I open the spa drain, the spa drains, and it does so rather quickly.
To answer your other questions:
Normal pool operation:
When in pool mode:
Water leaves the pool through the pool drain and the skimmer (as shown in the accompanying picture. The inlet labeled "To spa jets" is closed while in pool mode. NOTE: the diverter valve that controls the spa drain is usually a valve actuator. It "went" a few days ago, and I'm replacing it. Normally, it would automatically rotate 180 degrees from the position shown in the picture when switched from pool mode to spa mode. Right now, I'm doing that manually.
Water comes into the spa by way of a single inlet, labeled "To spa overflow". Water also enters the pool by way of floor pop ups (labeled in picture). The result: Water overflows the spa into the pool, as desired.
When in spa mode:
Water leaves the spa because the spa drain is now open. Water continues to leave the pool through the pool drain and skimmer. (I can manually shut either the pool drain or the skimmer, but not both. This has been the case for years. It stays in the position show (taking water in from both pool drain and skimmer, while in either pool mode or spa mode.)
Water comes into the spa by way of spa jets (labeled). No more "in" through spa overflow or floor pop ups.
As for the brand/model of the automation, all is controlled by a Waterways Plastics Oasis Pool and Spa control. The actuator valves are Hayward GVA24. There are two actuators. One that opens/closes the spa jets or spa overflow/pool floor pop ups (as shown), and the other that opens/closes the spa drain (controlled manually right now, but to be replaced).
As previously stated, all was working well, with these same valve settings, until a few days ago. I can confirm that the valve controlling the spa drain is indeed working. I manually turn it, and I can hear the water flow changing. Similarly, the valve controlling the spa jets into the into the spa is working.
I'm stumped and would appreciate any further thoughts you might have!
Thanks again.