Deciding how to distribute work between humans and AI systems is a central challenge in organisational design. Most approaches treat this as a binary choice, yet the operational reality is richer: humans and AI routinely share tasks or take complementary roles depending on context, fatigue, and the stakes involved. Governing that distribution -- balancing efficiency, oversight, and human capability -- remains an open problem. This paper presents Human-AI Adaptive Symbiosis (HAAS), an implemented framework for adaptive task allocation in software engineering and manufacturing. HAAS combines two coupled components: a rule-based expert system that enforces governance constraints before any learning occurs, and a contextual-bandit learner that selects among feasible collaboration modes from outcome feedback. Task-agent fit is represented through five auditable cognitive dimensions and a five-mode autonomy spectrum -- from human-only to fully autonomous -- embedded in a reproducible benchmark spanning both domains. Three empirical findings emerge. First, governance is not a binary switch but a tunable design variable: tighter constraints predictably convert autonomous AI assignments into supervised collaborations, with domain-specific costs and benefits. Second, in manufacturing, stronger governance can improve operational performance and reduce fatigue simultaneously -- a workload-buffering effect that contradicts the usual framing of governance as pure overhead. Third, no single governance setting dominates across all contexts; moderate governance becomes increasingly competitive as the learner accumulates experience within the governed action space. Together, these findings position HAAS as a pre-deployment workbench for comparing and inspecting human--AI allocation policies before organisational commitment.