This study introduces and investigates SRI-open sets as a new class of generalized open sets in ideal topological spaces. Their fundamental properties are established and supported by illustrative examples that clarify their behavior within the ideal framework. Several associated classes of functions are also examined, including SRI-continuous, strongly SRI-continuous, and SRI-irresolute mappings, together with their properties and relationships. Furthermore, new covering properties, namely SRI-compactness and SRI-Lindelöff spaces, are introduced and investigated, and their connections with the corresponding classical topological concepts are established. In addition, a new notion of connectedness, called SRI-connectedness via SRI-open sets, is defined and characterized through several equivalent results. The relationships between this generalized connectedness and classical connectedness are also discussed. The obtained results enrich the theory of ideal topological spaces, extending generalized topological structures and providing a broader framework for studying generalized open sets, generalized continuity, covering properties, and connectedness, offering promising directions for future research.