In the Space-Air-Ground Integrated Network (SAGIN), ground users exhibit high mobility and randomly generate heterogeneous computing tasks across different times and regions, posing significant challenges to dynamic perception and intelligent decision-making in Mobile Edge Computing (MEC) for task offloading and resource allocation. Given the limited computational resources of Unmanned Aerial Vehicles (UAVs) and satellite nodes, accurately identifying future congestion-prone areas and efficiently scheduling resources to minimize system cost becomes a key issue. To address this, this paper proposes an offloading optimization approach that integrates dynamic region partitioning, congestion prediction, and deep reinforcement learning (DRL). Specifically, an improved K-means algorithm is employed to dynamically cluster ground users, with each UAV acting as the cluster center to provide edge computing services. Considering the continuous mobility of users and highly variable task loads, a Long Short-Term Memory (LSTM) network is introduced to predict future congestion levels, which are then incorporated into the state representation to enhance the perception capability of the DRL policy. The Proximal Policy Optimization (PPO) algorithm is subsequently used to jointly optimize task offloading decisions and resource allocation strategies. The simulation results demonstrate that the proposed method effectively reduces the average user cost in the MEC system compared to three baseline algorithms.