Future 6G networks envision ubiquitous connectivity through space-air-ground integrated networks (SAGINs), where high-altitude platform stations (HAPSs) and satellites complement terrestrial systems to provide wide-area, low-latency coverage. However, the rapid growth of terrestrial devices intensifies spectrum sharing between terrestrial and non-terrestrial segments, resulting in severe cross-tier interference. In particular, frequency sharing between the HAPS satellite uplink and HAPS ground downlink improves spectrum efficiency but suffers from interference caused by the HAPS antenna back-lobe. Existing approaches relying on zero-forcing (ZF) codebooks have limited performance under highly dynamic channel conditions. To overcome this limitation, we employ a reconfigurable intelligent surface (RIS)-aided HAPS-based SAGIN framework with a deep deterministic policy gradient (DDPG) algorithm. The proposed DDPG framework optimizes the HAPS beamforming weights to form spatial nulls toward interference sources while maintaining robust links to the desired signals. Simulation results demonstrate that the DDPG framework consistently outperforms conventional ZF beamforming among different RIS configurations, achieving up to \(11.3\%\) throughput improvement for a \(4\times4\) RIS configuration, validating its adaptive capability to enhance spectral efficiency in dynamic HAPS-based SAGINs.