Depression is a serious psychiatric disorder that greatly impacts the quality of life and daily functioning of a person. Accurate diagnosis at the early stage is critical for success with intervention. Electroencephalography (EEG) offers a non-invasive technique to assess neurophysiological activity and is thus an important instrument for diagnosis of depression. Current EEG-based deep learning approaches are beset by high-dimensional data, poor feature selection, and poor classification performance owing to the nature of the EEG signal. To address these issues, we introduce EEGEffV2-SpikeNet, a new framework for depression detection that combines statistical feature extraction with deep feature extraction through a Graph Convolutional Network (GCN) approach. The proposed model incorporates a new fusion of statistical feature extraction and GCN-based deep feature learning for the extraction of both spatial and temporal EEG features. The extracted features are then optimized by the Modified Addax Optimization Algorithm (MAOA), a cutting-edge bio-inspired optimization algorithm that improves feature selection efficiency by discarding redundant information and enhancing classification accuracy. For depression classification, we utilize EfficientNetV2, Deep Belief Network (DBN), and Spiking Neural Network (SNN) to enhance feature representation and decision-making, leveraging the computational efficiency of EfficientNetV2 and the biologically plausible processing of SNN. Experimental results on two standard EEG datasets validate the better performance of the model, achieving 98.74% accuracy on Dataset 1 and 97.88% accuracy on Dataset 2, outperforming baseline models like DBN, EfficientNet, and SNN. The results prove the framework's promise as a dependable tool for objective and early depression diagnosis, with clinical application and mental health monitoring implications.