What dynamic state change in the solar system, facilitated by Jupiter, allowed Earth's biosphere to flourish beyond single-celled organisms?

The transition from a dynamically hot, unstable system to a cooler, more predictable one.

Jupiter played a crucial role in the maturation of the solar system environment by managing the early, chaotic bombardment phase. Initially, the early solar system was dynamically hot, characterized by frequent, violent collisions among planetesimals, which represented an existential threat to any developing life. Jupiter acted to clear space by either capturing these numerous objects or ejecting them entirely from the system. This sweeping action helped usher in a subsequent period that was significantly cooler, quieter, and far more predictable in terms of orbital mechanics. This transition to a quasi-stable environment provided the necessary extended period of relative calm required for the Earth's biosphere to move beyond simple, single-celled life and evolve into complex organisms.