Recent multilingual named entity recognition (NER) work has shown that large language models (LLMs) can provide effective synthetic supervision, yet such datasets have mostly appeared as by-products of broader experiments rather than as systematic, reusable resources. We introduce FiNERweb, a dataset-creation pipeline that scales the teacher–student paradigm to 91 languages and 25 scripts. Building on FineWeb-Edu, our approach trains regression models to identify NER-relevant passages and annotates them with multilingual LLMs, resulting in about 225k passages with 235k distinct entity labels. We train a student model on this dataset to enable the research community to efficiently expand annotations in their desired languages. The regression model for filtering useful NER passages achieves more than 84 F1. We assess annotation quality using LLM-based ratings, which show high faithfulness (3.99/5) and completeness (4.05/5). We further translate the label set into the respective target languages and observe a performance decrease of 0.02-0.09 F1. This result shows that many multilingual models rely heavily on English label prompts and that improved cross-lingual alignment is essential for future work.