So, is it the case that infinitely variable phase adjustment is in all aspects EXACTLY THE SAME THING as setting time delay in ms ?
That's quite a good and important question, and the answer is
no. The truth is that variable phase adjustment as usually found on subwoofer plate amps is technically
inferior to the time delay setting. The reason has nothing to do with "infinitely variable" vs "1 ms steps".
Subwoofers with a variable phase control knob implement an analogue
all-pass filter. It leaves the magnitude of the signal unchanged and just modifies the phase between 0⁰ and 180⁰. However, there is only one fixed corner frequency, defined as the frequency where the phase angle is 90⁰. The most important consequence is that you can set the 100% correct time shift (equalling the required delay) for
one frequency, only (usually 80 Hz). Everything far enough above or below the corner frequency is
not time-aligned with the other source, e.g. the main speakers.
This is just an approximation to the solution of the problem we want to solve, different time of arrival of sound waves due to either different distances to our ears or due to delay caused by processing (or both). Setting a latency in ms steps does exactly this, it compensates for a delay for
all frequencies. WiiM's chosen resolution of 1 ms is a tad rough, as each ms is equivalent to a distance of ~34 cm or ~12". It's still sufficiently precise compared to the wavelength at typical crossover frequencies (e.g. 4.3 m at 80 Hz). Personally, I'd be more happy with 0.5 ms steps, but I know that going all the way to 0.1 ms steps was probably necessary to silence all the critics.
The all-pass filter still works ok-ish (but not as well as the latency setting) in practice. The reason is the same as why 1 ms steps are usually fine enough: In the low bass and within a room we don't have to care about precision in the centimeter range.
Is it always going to be the higher frequency signal that requires the delay?
No, not always, but most of the time. In most domestic setups the subwoofer sits further from the listening position than the main speakers (in particular with corner placement, which makes a lot of sense if room correction is available). Also, modern subwoofers often use digital signal processing, adding further delay. Since there's no way to somehow speed up the signal from the sub, the mains must be delayed.
Note how this is not directly related to higher vs lower frequencies. You could end up with a setup where a purely analogue active subwoofer has no inherent delay and the sub actually sits closer to the listening position than the speakers (even though the acoustical center of the sub is almost never the center of the cone). In such a scenario it's possible that the subwoofer's signal needs to be delayed, but it's less common.
Can anyone point to resources that explain (ELI5) how to use REW to inform this?
Not from the top of my head, not sure if
@dominikz has already pointed to such a resource. Measuring the difference in timing directly is not that easy.
Personally I've always just followed the layman's approach of picking the setting that results in the highest SPL right at the crossover frequency.
Should the automatic process be run first, then manually just tweaked a bit?
Ideally, no manual tweaking should be necessary after using the automatic process, now that the correct microphone is used for the measurement. If the summation of mains and sub doesn't look smooth (e.g. when running RoomFit) it's certainly a valid approach to change the automatically obtained delay setting by +/- one or two milliseconds.
It's probably an even better idea to try out both “phase“ settings (0⁰ a d 180⁰) when measuring the delay. I'd go with whatever setting results in the smaller delay value.
The "phase" switch is actually a misnomer. It switches the polarity of the input signal, no all-pass filter in this case.
Is the process complicated by the fact that the stereo output signal gets further split downstream e.g. between my main bookshelf pair and midbass couplers use for bass reinforcement down to say 60-70Hz?
What are midbass couplers?

Sorry, looks like I didn't follow the changes to your setup on ASR as closely as I could have.