Reliable multi-bit watermarking is essential for tracing the provenance of large language model (LLM) outputs. However, existing high-capacity schemes typically synchronize pseudo-random functions through discrete token n-gram matching, which makes them vulnerable to desynchronization under semantics-preserving paraphrasing attacks. To address this issue, we propose HSPMark, a hierarchical semantic projection marking mechanism for context-aware multi-bit watermarking, which shifts watermark synchronization from brittle token histories to continuous semantic anchors. HSPMark extracts stable contextual features using a pre-trained sentence-level encoder and a lightweight Robust Semantic MLP, then projects these features into context-conditioned pseudo-orthogonal bias matrices for multi-bit payload injection. To balance payload capacity and generation quality, HSPMark introduces an entropy-adaptive embedding mechanism that modulates logit bias according to predictive uncertainty. Extensive evaluations demonstrate that HSPMark improves robustness against paraphrase-induced desynchronization and local perturbations while maintaining a competitive trade-off among bit accuracy, payload capacity, and text quality compared with existing high-capacity baselines.