The Web of Agents (WoA) transforms the document-centric Web into an environment of autonomous agents acting on users' behalf, a vision newly tractable as large language models (LLMs) mature. We argue that across three decades the WoA has undergone a \emph{semantic-effort migration} in chronological order: from platform-side coordination (Multi-Agent Systems, Generation~I), through data-side annotation (Semantic Web, Generation~II), to model-side interpretation (LLM-era, Generation~III). The central Gen~II~$\rightarrow$~Gen~III transition within this trajectory, which we call the \emph{semantics-in-data $\rightarrow$ semantics-in-models} shift, is predictive: each generation's failure modes and current open problems follow from where that generation located its semantic effort. The survey makes five contributions: (i)~a unified evolutionary narrative spanning 1990--2026; (ii)~a four-dimensional comparative framework (semantic foundation, communication paradigm, locus of intelligence, discovery mechanism) applied uniformly across all three generations; (iii)~classification of sixteen representative systems on these dimensions, including hybrid LLM--knowledge-graph and computer-use agents; (iv)~coverage of the November~2024--August~2026 institutional convergence (Linux Foundation's Agentic AI Foundation, A2A v1.0, MCP November~2024 launch and November~2025 specification, Visa/Mastercard/Stripe payment-network protocols, EU AI Act phased enforcement, the NIST AI Agent Standards Initiative, International AI Safety Report 2026); and (v)~seven named lessons grounded in cross-generational evidence paired with seven generation-invariant challenges that persist regardless of which protocol prevails. Further progress depends less on protocol design than on the socio-technical infrastructure now being assembled by standards bodies, regulators, and commercial payment networks.