Online safety in low-resource languages relies on effective hate speech detection, yet Bangla remains critically underexplored. Existing resources focus narrowly on binary classification and fail to capture the evolving, implicit nature of online hate. To address this, we introduce BanHate, a large-scale Bangla hate speech dataset, comprising 19,203 YouTube comments collected between April 2024 and June 2025. Each comment is annotated for binary hate labels, seven fine-grained categories, and seven target groups, reflecting diverse forms of abuse in contemporary Bangla discourse. We develop a tailored pipeline for data collection, filtering, and annotation with majority voting to ensure reliability. To benchmark BanHate, we evaluate a diverse set of open- and closed-source large language models under prompting and LoRA fine-tuning. We find that LoRA substantially improves open-source models, while closed-source models, such as GPT-4o and Gemini, achieve strong performance in binary hate classification, but face challenges in detecting implicit and fine-grained hate. BanHate sets a new benchmark for Bangla hate speech research, providing a foundation for safer moderation in low-resource languages. Our dataset is available at: https://huggingface.co/datasets/aplycaebous/BanHate.