Web services increasingly expose backend interfaces that let users delegate tasks to AI agents, which invoke service operations directly without navigating websites. This shift changes how existing Web vulnerabilities can be exploited. We investigate these changes through VELA, an executable benchmark covering 44 vulnerabilities across twelve Web application families. The benchmark preserves vulnerable backends and derives agent-facing interfaces from legitimate workflows. We evaluate three commercial agents across multiple interface configurations, using controlled comparisons to separate interface effects from agent behavior and independent oracles to verify attack outcomes. Our results show that the agent realizes every attack that direct interface invocation realizes in the reference configuration, so exploitability is set mainly by the interface: 91% of vulnerabilities remain exploitable under the reference design. Interface restrictions prevent some attacks by removing required operations or limiting input control, while retention remains high across vulnerability classes. No case-level loss in the reference configuration is attributed to agent refusal or input normalization, and in one case the agent completed an attack by supplying calls the attacker omitted. Across the tested configurations, interface design affects exploitability more than agent choice, moving retention from 39% to 95% against at most 4.5 points across agents, but some restrictive interfaces also limit legitimate workflows. Our study provides a systematic empirical account of how agent-mediated access reshapes existing Web vulnerabilities, grounding future Web architecture design in measured security outcomes and trade-offs between reducing attack exposure and preserving legitimate functionality in agent-facing services.

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