Best idea is to flush the cooling system, maybe more than once or twice, running the water with a very mild flushing compound for a day or so before draining. After that, when it seems to be clean, fill with water and a rust inhibitor only, observe, and see if more appears. If not, after an appropriate period, refill with SCA-laced coolant, go forth and make some black smoke.
With no clear direction, always start with the least expensive step. Potentially, leaking oil cooler seals can put oil in the cooling system and coolant in the oil almost simultaneously. When the engine is running, oil pressure is higher and oil goes into coolant. Shut the engine off and the reverse happens. I have never faced this problem with my own truck (though I have resealed the cooler, plus decades of professional wrench twisting experience) and the best approach is the a calm, methodical and measured one. Step by step. Start with the most likely and least expensive answer (unless another answer comes out to bite you in the ass) and work your way down the list of possibilities in order of likelihood and the evidence presented. Otherwise, you are running around, stepping on your crank and making it just about impossible to pinpoint the problem and make a pinpoint repair.
The most likely answer is that whoever did the cooler repair did a poor job of cleaning out the cooling system. There are increasingly more dire possibilities that you'll have to work your way thru if the oil continues to appear. It isn't unknown for seals to be damaged while resealing a cooler, so don't necessary discount the idea of tearing the cooler apart again.
I have found small oil cooler leaks in other engines by draining the oil when the engine is really warm. Then move the oil pan out of the way and place an empty one there, put the cooling system under pressure with a pressure tester and keeping it pressurized for a long time. On a good cooling system, it should hold pressure for a long time and only very slowly leak down. If you have a cooler leak, the pressure will drop more quickly and eventually water will dribble down into the pan and out into the pan.