To echo what the others have said, when you see the super slim bikepacking setups that other people have, keep in mind that they are bringing the most minimalist possible gear, and even then, often their bags will be bursting at the seems. If you are looking to bring climbing gear with you, you are very likely going to need some big panniers for rope and harnesses and such. A good experiment would be to put all your gear in a big pile and measure the volume of it. That will guide you towards how many bags, and how big of bags, you need. I'd hate for you to dump a ton of money into super streamlined bikepacking bags only to find you need a setup with 3x the volume.
For reference, after a bit of googling around, this is what one person ended up needing for a bikepacking/climbing trip
https://www.reddit.com/r/bikepacking/comments/7njtsy/my_first_try_at_combining_my_two_hobbies_was_a/Then again these guys did it with a kid and only needed 2 trailers and 2 backpacks between the 3 of them.
https://www.sidetracked.com/le-tour-des-alpilles/