If you go down to the monkey, see the grapple point, you grapple to it, the snake attacks, and while you’re in midair, you need to maneuver yourself so you fall back down past the bridge without getting hit, grapple back up, then rush into the doorway. Might take you a try or two, but it’s very doable.
https://www.reddit.com/r/Sekiro/comments/b6gxvw/is_there_a_way_to_get_past_the_snake_in_sunken/