It even sort of reads as though he pretty deliberately orchestrated the entire thing at least partially to encourage a sense of competition and jealousy between them
That's one way to read it. I prefer the reading where he was trying to forge a bond between them by throwing them at each other before getting them to unite forces against Alfred/Two-Face. I may be pushing it, but it's a reading that's encouraged, I think, by the numerous references Dick makes to being 'partners' and 'teamwork' in the last chapter. I had to leave it out, but there's a page showing Dick, Jason, and Babs, and the narrative boxes ask what Robin is about, if it's about making a partner, or making a team - which is a befuddling way to think about Robin, but it raises the question.
Then again, Bruce acting immature and unfair and selfish is always going to be preferable for me to the version of Bruce that could actually tell Dick he'd only taken Jason in because he missed Dick. Bruce's never been at his best when Robins change.
at least to shove the appropriation of Robin by someone else in Dick’s face and hurt him with it as much as possible
Not trying to justify it, but I think if it's what he wanted to do, it's probably been prompted by Dick acting out in Gotham.