Precisely detecting multi-stage degradation (MD) in rolling bearings is crucial for keeping equipment in good shape. Yet, health indicator (HI) crafted with current single-method strategies often can't balance degradation sensitivity and monotonicity across different operating conditions. Also, common MD detection methods struggle to spotransitional samples between degradation stages in cross-condition settings. To tackle these challenges, this paper introduces a new cross-condition MD detection approach for bearings, which relies on a health indicator matrix (HIM) and a transition sample enhanced network with multi-branch encoding (TSEN-MBE). First, a degradation-sensitive health indicator (DSHI) is constructed by integrating the least absolute shrinkage and selection operator (LASSO) algorithm — with comprehensive fault frequency energy (CFFE) as the regression target — and the grey wolf optimizer (GWO), capturing intrinsic degradation characteristics of bearings. Meanwhile, to enhance the monotonicity of unsupervised HIs, a time-weighted Wasserstein distance (TWWD) metric is proposed by incorporating temporal degradation features into the Wasserstein distance-based HI construction. The DSHI and TWWD are subsequently combined to generate the HIM. This HIM serves as the driving force for the Gath-Geva (GG) fuzzy clustering algorithm, enabling it to adaptively allocate MD labels according to varying operating conditions. Ultimately, the TSEN-MBE model is constructed, employing multi-branch Transformer encoders integrated with multi-head attention mechanisms to encode and combine heterogeneous features. A joint loss (JL) function — comprising transition sample enhancement (TSE), local maximum mean discrepancy (LMMD), and cross-entropy (CE) losses — is designed to enhance the recognition of transitional samples and improve cross-condition MD identification accuracy. Experimental results on the XJTU-SY dataset validate the effectiveness and superiority of the proposed method, showing that DSHI achieves the highest average degradation angles, TWWD obtains optimal monotonicity, and TSEN-MBE outperforms comparative methods in cross-condition recognition tasks.