Reading this, I am wondering about the dive conditions. Can you see the bottom from the surface? Looking for a dive buddy often times is about finding out which one of your blind spots he is sitting in, not that he he really lost. When vis is low, I will turn on one of my dive lights and let it burn, even if I am not using it. A dive light will illuminate particulates in the water making you much easier to see from a distance. A dedicated tank beacon can do this, but lack brightness for really crappy visibility. A pop up to find your buddy is going to cut into you air supply because you need to release air from your BCD, then add it back at depth. My first step is to wave my light around and look for his (he does the same). We are seldom in visibility greater 15’
Doing a safety stop while floating in open water, while a best practice, may not be a great idea if there is a possibility of a current. After 3 minutes you may find your self a disturbing distance from your boat, and everything looks even farther when your head is six inches above the surface. Generally, for a missing diver situation, I would skip the 3 minutes if you are going to descend again Immediately. A “meet-up” location like the anchor line or easy to find topographic spot that is predetermined. If you do the safety stop, shoot a marker so if the current takes you, the boat can see you.