Given that the purpose of separation standards is collision avoidance, I don’t understand your distinction. Are you saying that once a pilot declares a go-around, ATC is no longer obligated to apply separation standards?
The 7110.65/5-8-4 (radar departures)......
I'm not sure that it's quite as straightforward as separation is done for collision avoidance, perhaps more for 'an orderly and expeditious flow of air traffic', and it's done by ATC. Collision avoidance is different and both pilots and ATC have obligations - conflating the two is unlikely to aid understanding.
As for the US rules, I'm afraid I'm not very familiar with them, but in terms of separation, section 7-2-1 could also be applicable (although without hearing full recordings it's not clear that all of the conditions were complied with). But the reality in this type of situation is that standard separation has become secondary and collision avoidance is the primary objective. The instructions to the aircraft going around whether to go left or right really doesn't make much difference during the critical period. I've no idea what equipment is available to the tower controller at KMSP to monitor where the aircraft are but I would be surprised if there is no form of radar-derived display of the airport and its surroundings, whatever, I can't help feeling a larger heading split might have been better if it had been possible (maybe traffic on other runways limited such an option). It surprises me also that on the recordings that we have that the pilots of the aircraft involved don't appear to have more interest in where they each are. Likewise, the controller doesn't sound in the slightest concerned about the developing traffic situation - is this something that happens every day?
All of this is just armchair analysis, of course, and I can't see what Gne has posted as the FAA's response, but one would hope that a proper investigation is done and that something is learned from the debacle.