Language Model (LM)-based generative modeling has emerged as a promising direction for TSE, offering potential for improved generalization and high-fidelity speech. We propose GenTSE, a two-stage decoder-only generative LM for TSE: Stage-1 predicts coarse semantic tokens, and Stage-2 generates fine acoustic tokens. Separating semantics and acoustics stabilizes decoding and yields more accurate target speech. Both stages use continuous SSL or codec embeddings, offering richer context than discretized-prompt methods. To reduce exposure bias, we employ a Frozen-LM Conditioning training strategy that conditions the LMs on predicted tokens from earlier checkpoints to reduce the gap between teacher-forcing training and autoregressive inference. We further apply DPO to better align outputs with perceptual preferences. Experiments on Libri2Mix show that GenTSE surpasses previous LM-based systems in speech quality, intelligibility, and speaker consistency.