I spent 20 years and well over 1500 dives in mostly low viz. What to do in the event of a separation was not an academic argumet, but rather a frequent occurrence.
In some cases (realistically most cases, if the buddy was experienced) I and my buddy would decide before hand that in the event of a separation, we would continue separately as solo divers. That has to be decided in advance so that each diver can properly configure their gear and do the gas planning, ensure adequate redudancy and ensure each maintains their own situational awareness and navigation.
In other cases, the plan would be to locate each other. However, this approach works best if you have a lead diver and a trailing diver. The dive plan also has to get thoroughly discussed in advance (max depths, times, turn points, landmarks, etc. During the dive the lead diver ensures any change in course during the dive is comunicated to the trailing diver and that they are indeed following after the course change. With that in place, the idea of having a base course that you are both on gives you a more targeted area to search in the event you do become separated.
If you have to ascend after an unsuccessful attempt to rejoin underwater, look for bubbles on the way up. The viz is often better off the bottom and it makes mores sense to follow the bubbles back down from mid ascent than to go all the way to the surface.
With regard to a safety stop, if I am close to an NDL I am going to take it. If I am diving in a current, odds are I started the dive swimming into it, so I will be drifting back down my course line and if the buddy is in trouble on the bottom, I am possibly going to spot the bubbles during the stop. More so even than on the surface if the condtions are choppy.
If the buddy is in trouble on the surface, the immediate threat is less and and extra 3 minutes is probably not going to be vital. If it is a coronary, CPR on the surface in the water is very ineffective anyway, so unless I could have potentially gotten the ashore or on board in a few minutes, it is a moot point whether I take a safety stop or not. Better to be safe and avoid a second victim.
If the buddy just got lost and surfaced (by far the most likely scenario) they will still be there after 3 minutes, or they will see my bubbles after they complete their safety stop and surface and swim down to me and we can then either continue the dive or abort. If I am diving deep (90-130 ft) and have to surface, the dive is for all intents and purposes over even if we were only on the bottom for a couple minutes.
Where it gets interesting is if you surface and the buddy is not there in a situation where the water is deep. They may have decided not to surface or may just be taking their own safety stop in which redescending places you at unwarranted risk. On the other hand, they may be entangled on the bottom and rapidly running out of air in which case they die if you don't redescend to find them.
In light of that I will swim a pattern to look for bubbles on the surface (taking the current into account - and also recognizing that in a strong current you may not be able to return to a spot over an entangled diver) but will not redecend unless I see bubbles.
In any event preveting a separation is much more productive than dealing with a separation, Similarly, locating each other underwater is the quickest way to render assistance, so having solid search protocols for lead and trail divers to improve the odds of rejoining underwater is important. It is also vital that both divers know the protocol and follow it to avoid putting the second diver at uneccesary risk if they have to surface.
And there are variations depending on the equipment in use. For example if a dive flag law requires the diver to tow a flag, the flag towing diver is readily marked and easy to locate on the surface. In that case the protocol in shallowish water (30-60 ft) maybe for the separated diver to surface, locate the flag and signal the submerged diver with a tug when they find the flag and then descend along the flag line and resume the dive. If the surfaced diver needs assistance they can give several rapid tugs, and vice versa, the surfaced diver can be advised of a problem below by either a lack of an answering tug or by a series of rapid tugs.
On a deeper dive with a dive flag, if the surfaced diver elects to stay surfaced they can provide an ok signal through the line and then communicate that they will stay on the line until the submerged diver surfaces after a safety stop. You just need to work out the protocol and signals in advance. In really low viz this may be reason enough to have the lead diver tow a flag or SMB.
In technical diving it is common in some locations for a yellow lift bag to mean one thing and an orange lift bag to mean another with one being "OK" and the other meaning "I have a problem and need assistance". A similar approach makes sense in a recreational setting in deeper water to facilitate relocating each other and helping a surfaced diver tell the difference between a diver on a safety stop and a diver in trouble on the bottom. At a minimum an SMB makes it easier for one diver to notice and locate another diver who is not yet on the surface.
In short the PADI "search for one minute and then surface" protocol works ok for dives to 60 ft or so that are well within the NDL's but it gets problematic as you go deeper or stay longer and frankly I don't think it was ever really intended to be the only separation plan once you start venturing below the 60 ft domain of the OW diver. At the AOW level, you need to have more skills and a better plan that utilizes additional resources as above all else, assisting one diver should not place another diver at undue risk as we already have way to many fatalities in this sport that needlessly become double fatalities.