It would be extremely inappropriate and unreliable to scale Superman from a crossover with another verse that also only involved the alternate Injustice version of Superman, and as such also likely should have no bearing on regular canon.
I am not that invested in upgrading New-52 Superman; however, before dropping the subject I am going to make some comments on the issue.
Firstly, the Injustice Versus Masters of the Universe you mention is the wrong crossover. (As a side point there are multiple versions of the Injustice universe existing within the multiverses of The Divine Continuum: the original video game version which has its own supporting / backup comics, the recent version in the mainstream multiverse that Jon Kent encountered, and the version from Injustice Versus Masters of the Universe which is a variant of Injustice Superman where the bad ending occurs from the end of the Injustice 2 video game.)
Back to the main point regarding the usage of this crossover. The reason why I have included He-Man information as evidence for 2A New-52 Superman / herald characters is multifold.
Firstly, Masters of the Universe was licensed for publication by DC at the time. DC was publishing other Masters of the Universe comics at the same time besides the crossover comic. It is not as if the crossover was occurring between two separate publishers like Dark Horse or Marvel for example.
Secondly, and more importantly, because the events of the DC cross over DIRECTLY impact and are CANON to the corresponding Masters of the Universe comic that was being published by DC at the same time: He-Man Eternity War. In issue #5 of Eternity War, Skeletor directly states how his banishment into Hypertime by John Constantine has radically altered his outlook on reality and has driven him to insanity. Later in the Eternity War series this is shown as he is driven to end everything since he saw in Hypertime, while banished there, that there is NO reality in which he ever wins as such he decides if he cannot win then neither can anyone else. This is a fundamental plot point to the entire He-Man Eternity War comic series. There was even a text note in one of the He-Man Eternity War comics to tell readers to check out the crossover so they Ould have more context for the story.
Thirdly, while New 52 Superman and other New 52 characters do not show the same level of feats as their Post-Crisis versions, they really should not be AS far behind from them as they are currently depicted on this wiki. It is worth mentioning that this is most likely simply a result of the New-52 only lasting from 2011 to 2016 as such the writers did not have much time to provide him with any super high tier feats. When Doctor Manhattan removed 10 years of history and erased the Justice Society of America this results in New-Earth / Earth-0 (The Post-Crisis reality) becoming Prime-Earth creating the New-52. Removing 10 years of history should not necessarily prevent Superman from being 2A at maximum in the New-52. It is important to remember that Prime-Earth IS New-Earth but with the time manipulations of Doctor Manhattan. A counter argument would be that Superman in the New-52 simply has not had time to grow into 2A power levels the way he did in Post-Crisis, but I think, at the very least, it should be considered. This can be seen that even Post-Crisis Superman (Pre-Eradicator Absorption) was capable of 2A feats as such it is logical that New-52 Superman is capable of the same thing (at the moment Post-Crisis Superman and many other previously 2A characters were incorrectly changed to low-1C; however, Post-Crisis Superman like most of the previous 2As should not have been amongst those changed so he will be returning to 2A. This is something I will address in my up coming Heralds and low level cosmic beings revision.) I would suggest putting New-52 Superman's statistics as (Varies, usually 4B up to 2A.) This provides a logical continuity of power between the eras of Superman from Post-Crisis to New-52 continuing into Rebirth.
My last point is on crossover in general, I agree that crossovers should almost never be used; however, like with most things there are exceptions and I think there is plenty of evidence here to show that this is one of them. Another example of the events of a crossover being canon to a character is Krona, who at the end of JLA/Avengers ends up inside a Cosmic Egg, this plot line DIRECTLY carries over into the story of Trinity Volume 1.