Zero-shot graph learning (ZGL) is essential in many real-world applications, where models are expected to generalize to unseen graph structures and label distributions without task-specific fine-tuning, enabling knowledge transfer across diverse and evolving graph domains. Despite progress in graph representation learning, extracting universal task-agnostic features remains challenging, hindering plug-and-play zero-shot generalization across graph domains. To address this gap, we present ScaleGraph, a scalable self-supervised framework that alleviates feature misalignment, structural heterogeneity, and domain bias through three key innovations: (1) a parameter-free graph tokenizer that aligns heterogeneous feature spaces across domains via nonlinear kernel mapping, (2) a hierarchical transformer with linear attention that captures multi-scale structural dependencies, and (3) a lightweight classifier scheduler that achieves meta-learned domain adaptation through optimal transport. Extensive experiments demonstrate that ScaleGraph achieves state-of-the-art (SOTA) performance on cross-domain node classification and link prediction, highlighting its strong adaptability and effectiveness for zero-shot graph learning.