This scene was incorporated so they can draw from it later in the movie.
His parent's death....he falls into the cave and "rises" *its a dream*
The following scene is the attack on Metropolis and shows the first time he's feels helpless since his parents death.
This time he falls and does not do Batman like things. Only until finding humanity in Superman that he rises and becomes Batman again.
I think it gets better on multiple viewings. But I can see how you feel that way about how the story is unfolds.
You get it bruh.
This is pretty much how I saw it. Batman was broken (they've mentioned this plenty times). He felt powerless and hopeless not just with Superman... In general. Felt like all the shyt he's done in 20 years couldn't save his parents, couldn't save Robin, and then couldn't save the employees at the Wayne tower. That's why he was kinda a brutal a$$hole with a drinking problem... The drinking being the main clue to dude no longer giving a fukk as much
He saw Superman as another reason he will become powerless and chose to obsessively stop him however he could..
Lex was more envious than Bruce was. He wanted to feel as powerful as Superman and destroying Superman (whether it came from Batman or Doomsday) was the key to becoming what Superman is... Which is damn near a god.
While Superman just wanted to do what's right and just but realized that the world is never going to make that easy. No matter what he did it became scrutinized... Even if he wasn't the one doing it. After the bombing of congress he was pretty much done with everything and went into seclusion. He didn't know if he was helping the world or hurting it.
I loved the movie honestly. All you had to do was put yourself in relatable shoes. Even Lex became more like able once you understood all the riddles he was throwing out left and right.