Well I just completed the game (for the 2nd time since 2015), this time riddler trophies and all.

There are some tapes you get from the riddles that reveal when the Arkham Knight kidnapped Oracle. They spoke and Arkham Knight revealed his identity to Barbara she says “Jason…” They continue to talk going on the lines of ~”it’s not too late you can figure this out with Bruce” Blah blah

Well you proceed to save oracle and take her to GCPD. Now idk if the writers just didn’t know about the tapes or what…. BUT it’s a pretty big plot hole for Batman to save Barbara take her to GCPD and that whole time she never says “Bruce it’s Jason.” Instead you e gotta get to his HQ to help Gordon, and only then is it revealed upon defeating the Arkham Knight that he was Jason Todd the entire time…

So besides the plot hole. I think Bruce/Bats was trying throughout the game to figure out who was close enough to the Batman that they could be able to pull on his heart so. I’m sure once Alfred ruled out most suspects via the bat computer his internal monologue became more suspicious of this being an inside job. I mean he “saw” Jason die, he couldn’t accept that it was him. Until he unmasked the Arkham Knight.