Electroencephalography (EEG) is the cornerstone of non-invasive brain-computer interfaces (BCIs), yet conventional decoding relies on fragmented, task-specific architectures that severely limit cross-task scalability. While EEG foundation models pre-trained on massive corpora promise universal brain decoding, current post-training depends on task-isolated fine-tuning. This static paradigm restricts knowledge transfer across heterogeneous tasks, hinders model scalability, and incurs computational and storage overheads that scale linearly with task count. To overcome these bottlenecks, we formulate downstream adaptation as a cross-task continual learning problem and propose EvoBrain, a dynamic, task-aware continual learning framework for unified EEG decoding. EvoBrain addresses the plasticity-stability trade-off via two complementary components: (1) Neuro-Spectral Task Normalization (NSN) aligns incoming tasks with historical statistics while recalibrating spectral responses to handle distributional and neuro-spectral shifts; and (2) Response-Affinity Distillation (RAD), combined with time-dependent replay, preserves old-task response geometry and promotes selective knowledge transfer between spectrally compatible tasks, effectively mitigating forgetting. Extensive evaluations across six distinct BCI tasks demonstrate that EvoBrain consistently surpasses state-of-the-art methods across diverse foundation backbones, optimally balancing plasticity and stability. To our knowledge, this work pioneers cross-task continual learning in the EEG domain, advancing the realization of a unified, one-for-all brain decoding system.