Policy Gradient Estimate under Uniform Trajectory Probability

In policy gradient methods, the gradient of the log-probability of a trajectory is initially expressed as the sum of two components: one related to the agent's actions and another related to the environment's transitions. The expression is then simplified by removing the environment's component before optimization. Given the initial expression: $\frac{\partial}{\partial \theta} \left[ \sum_{t=1}^{T} \log \pi_{\theta}(a_t|s_t) + \sum_{t=1}^{T} \log \text{Pr}(s_{t+1}|s_t, a_t) \right]$ What is the fundamental assumption that justifies simplifying this to just the policy component, $\frac{\partial}{\partial \theta} \sum_{t=1}^{T} \log \pi_{\theta}(a_t|s_t)$?

Applicability of Policy Gradient Methods

Practical Implications of the Policy Gradient Simplification