Empathy is increasingly recognized as a key factor in human-AI communication, yet conventional approaches to "digital empathy" often focus on simulating internal, human-like emotional states while overlooking the inherently subjective, contextual, and relational facets of empathy as perceived by users. In this work, we propose a human-centered taxonomy that emphasizes observable empathic behaviors and introduce a new dataset, Sense-7, of real-world conversations between information workers and Large Language Models (LLMs), which includes per-turn empathy annotations directly from the users, along with user characteristics, and contextual details, offering a more user-grounded representation of empathy. Analysis of 695 conversations from 109 participants reveals that empathy judgments are highly individualized, context-sensitive, and vulnerable to disruption when conversational continuity fails or user expectations go unmet. To promote further research, we provide a subset of 672 anonymized conversation and provide exploratory classification analysis, showing that an LLM-based classifier can recognize 5 levels of empathy with an encouraging average Spearman $ρ$=0.369 and Accuracy=0.487 over this set. Overall, our findings underscore the need for AI designs that dynamically tailor empathic behaviors to user contexts and goals, offering a roadmap for future research and practical development of socially attuned, human-centered artificial agents.