Generative AI (GenAI) has become part of the technology landscape for many deaf people, marking potential shifts in daily communication, access, and agency. Yet, little is known about how deaf people interact with GenAI. In response, we conducted a multilingual online survey with 235 participants across Europe and five semi-structured interviews; our qualitative analysis focuses on the signed video responses from eight survey repondents together with the interviews, exploring how deaf people interact with, experience, and make sense of the LLM-based system ChatGPT. Our findings show that deaf people use ChatGPT as both a digital and language assistant in everyday contexts, reducing their reliance on human assistance. These practices are not only pragmatic but also shaped by prevailing language ideologies, bringing a sense of agency while at the same time creating new forms of (in)dependency and (hidden) access labor. This study contributes a socio-technical understanding of the role of AI in deaf communication and access.