本地部署的智能研究代理会泄露用户隐私，因网络行为有独特模式可被追踪。

We show that Web and Research Agents (WRAs) -- language-model-based systems that investigate complex topics on the Internet -- are vulnerable to inference attacks by passive network observers. Deployment of WRAs \emph{locally} by organizations and individuals for privacy, legal, or financial purposes exposes them to DNS resolvers, malicious ISPs, VPNs, web proxies, and corporate or government firewalls. However, unlike sporadic and scarce web browsing by humans, WRAs visit $70{-}140$ domains per each request with a distinct timing pattern creating unique privacy risks. Specifically, we demonstrate a novel prompt and user trait leakage attack against WRAs that only leverages their network-level metadata (i.e., visited IP addresses and their timings). We start by building a new dataset of WRA traces based on real user search queries and queries generated by synthetic personas. We define a behavioral metric (called OBELS) to comprehensively assess similarity between original and inferred prompts, showing that our attack recovers over 73\% of the functional and domain knowledge of user prompts. Extending to a multi-session setting, we recover up to 19 of 32 latent traits with high accuracy. Our attack remains effective under partial observability and noisy conditions. Finally, we discuss mitigation strategies that constrain domain diversity or obfuscate traces, showing negligible utility impact while reducing attack effectiveness by an average of 29\%.