Social cues, which convey others' presence, behaviors, or identities, play a crucial role in human information seeking by helping individuals judge relevance and trustworthiness. However, existing LLM-based search systems primarily rely on semantic features, creating a misalignment with the socialized cognition underlying natural information seeking. To address this gap, we explore how the integration of social cues into LLM-based search influences users' perceptions, experiences, and behaviors. Focusing on social media platforms that are beginning to adopt LLM-based search, we integrate design workshops, the implementation of the prototype system (SoulSeek), a between-subjects study, and mixed-method analyses to examine both outcome- and process-level findings. The workshop informs the prototype's cue-integrated design. The study shows that social cues improve perceived outcomes and experiences, promote reflective information behaviors, and reveal limits of current LLM-based search. We propose design implications emphasizing better social-knowledge understanding, personalized cue settings, and controllable interactions.