Collecting living species out of selfish urges for acquisition or scientific curiosity is not a part of Superman, these, we are led to believe, are creatures that he has either rescued from extinction or is safekeeping until he can relocate. That in itself seems at odds with Superman's disinterest and/or inability to get out into space, but this is the problem with a character who hasn't been thought out properly and writers who are honouring his Silver-Age past without thinking of the implications of reintroducing an element like this.
You might think Superman would liaise with Green Lantern over the issue...
Think that all highlights that Rebirth needs to end with him having all ofhis past restored now into his history... And do think that would be an interesting take on him, as maybe in the future after Lois dies and he lives earth to Jon, that he would search universe to save soecies, and stop those from destroying them? maybe like a type of Watcher who would intervent when needed?