Integrated sensing and communication (ISAC) represents a key paradigm for future wireless networks. However, existing approaches require waveform modifications, dedicated pilots, or overhead that complicates standards integration. We propose sensing for free - performing multi-source localization without pilots by reusing uplink data symbols, making sensing occur during transmission and directly compatible with 3GPP 5G NR and 6G specifications. With ever-increasing devices in dense 6G networks, this approach is particularly compelling when combined with sparse arrays, which can localize more sources than uniform arrays via an enlarged virtual array. Existing pilot-free multi-source localization algorithms first reconstruct an extended covariance matrix and apply subspace methods, incurring cubic complexity and limited to second-order statistics. Performance degrades under non-Gaussian data symbols and few snapshots, and higher-order statistics remain unexploited. We address these challenges with an attention-only transformer that directly processes raw signal snapshots for grid-less end-to-end direction-of-arrival (DOA) estimation. The model efficiently captures higher-order statistics while being permutation-invariant and adaptive to varying snapshot counts. Our algorithm greatly outperforms state-of-the-art AI-based benchmarks with over 30x reduction in parameters and runtime, and enjoys excellent generalization under practical mismatches. Applied to multi-user MIMO beam training, our algorithm can localize uplink DOAs of multiple users during data transmission. Through angular reciprocity, estimated uplink DOAs prune downlink beam sweeping candidates and improve throughput via sensing-assisted beam management. This work shows how reusing existing data transmission for sensing can enhance both multi-source localization and beam management in 3GPP efforts towards 6G.