At this point Bruce was Tim legal Guardian not adoptive parent according to tec, Jason was Bruce's foster kid not adoptive son [this was prior to the King Batman issue the re-established that Dick was adopted so at the time Damian was Bruce's only legal son.
I saw a lot of people complaining about that and others defending it as Damian being the only one related to Thomas by Blood but the truth was that in canon [Rebirth tec and rebirth RHATO] the status of the bat family changed.
That not true about Snyder's Batman. Snyder said that Damian reminds him of his kid which was why he couldn't write him
This is backed up by Morrison and Tomasi
Tomasi said that he knows Scott thinks Robin is irresponsible and something Bruce would never do.
Morrison laughed at the idea of Snyder having to write Damian since one of the reasons why he wanted to put his toys back in the box was because Scott likes Batman without alone.
Snyder made the decision not to have Damian in his Batman run not DC.