In Vitro and In Silico Activities of <i>E</i>. <i>radiata</i> and <i>E</i>. <i>cinerea</i> as an Enhancer of Antibacterial, Antioxidant, and Anti-Inflammatory Agents

<i>Eucalyptus</i>, a therapeutic plant mentioned in the ancient Algerian pharmacopeia, specifically two species belonging to the <i>Myrtaceae</i> family, <i>E</i>. <i>radiata</i> and <i>E</i>. <i>cinerea</i>, were investigated in this study for their antibacterial, antioxidant, and anti-inflammatory properties. The study used aqueous extracts (AE) obtained from these plants, and the extraction yields were found to be different. The in vitro antibacterial activity was evaluated using a disc diffusion assay against three typical bacterial strains. The results showed that the two extracts were effective against all three strains. Both extracts displayed significant antioxidant activity compared to BHT. The anti-inflammatory impact was evaluated using a protein (BSA) inhibition denaturation test. The <i>E</i>. <i>radiata</i> extract was found to inhibit inflammation by 85% at a concentration of 250 µg/mL, significantly higher than the Aspirin. All phytoconstituents present good pharmacokinetic characteristics without toxicity except very slight toxicity of terpineol and cineol and a maximum binding energy of −7.53 kcal/mol for its anti-TyrRS activity in silico. The study suggests that the extracts and their primary phytochemicals could enhance the efficacy of antibiotics, antioxidants, and non-steroidal anti-inflammatory drugs (NSAIDs). As pharmaceutical engineering experts, we believe this research contributes to developing natural-based drugs with potential therapeutic benefits.