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note that if you do have issues with the voltage fluctuating when the relay switches, you can often connect a ceramic capacitor across the coil contacts of ~1uF along with a small diode acting as a flyback connected in reverse polarity, and it's enough to smooth out a good bit of that draw and/or switch-off flux pulse. Filtering saves lives

Thanks, I don't think there are any external settings for the power supply, but it does provide a few more volts than I strictly need. Toggling a single relay hasn't caused me any issues in the limited testing I've done. A momentary drop to as low as 5V should be perfectly fine, although, looking over the specs for my components, I see I'm getting dangerously close to the upper limits for the power supply's current rating. I'll have to look into connecting 2 supplies in parallel (or getting a larger supply) I suppose.

I haven't worked with battery backups yet, so I was thinking it would be best to keep that element simple to minimize potential issues like a trickle charge draining the battery unexpectedly, or damaging the battery from overcharge. The minimum requirement is just to ensure the hardware (a motorized ball valve) returns to a closed position if power is lost. The battery needs to provide at least 9V to power the motor, so I could use a 9V (or a few smaller cells in series) to keep it below the 12V supply.

With your solution using a diode on each voltage source, would there be any risk of a trickle charge draining the battery unexpectedly if the battery? If so, in that configuration I'd need to do more research and figure out how to use a BMS, rather than an externally recharged or disposable cell.