Following the 2024 U.S. presidential election, Democratic lawmakers and their supporters increasingly migrated from mainstream social media platforms like X (formerly Twitter) to decentralized alternatives such as Bluesky. This study investigates how Congressional Democrats use Bluesky to form networks of influence and disseminate political messaging in a platform environment that lacks algorithmic amplification. We employ a mixed-methods approach that combines social network analysis, exponential random graph modeling (ERGM), and transformer-based topic modeling (BERTopic) to analyze follows, mentions, reposts, and discourse patterns among 182 verified Democratic members of Congress. Our findings show that while party leaders such as Hakeem Jeffries and Elizabeth Warren dominate visibility metrics, overlooked figures like Marcy Kaptur, Donald Beyer, and Dwight Evans occupy structurally central positions, suggesting latent influence within the digital party ecosystem. ERGM results reveal significant homophily along ideological, state, and leadership lines, with Senate leadership exhibiting lower connectivity. Topic analysis identifies both shared themes (e.g., reproductive rights, foreign conflicts) and subgroup-specific issues, with The Squad showing the most distinct discourse profile. These results demonstrate the potential of decentralized platforms to reshape intra-party communication dynamics and highlight the need for continued computational research on elite political behavior in emerging digital environments.