New Antibacterial Secondary Metabolites from a Marine-Derived Talaromyces sp. Strain BTBU20213036

New polyketide-derived oligophenalenone dimers, bacillisporins K and L (1 and 2) and xanthoradone dimer rugulosin D (3), together with four known compounds, bacillisporin B (4), macrosporusone D (5), rugulosin A and penicillide (6 and 7), were isolated from the marine-derived fungus Talaromyces sp. BTBU20213036. Their structures were determined by detailed analysis of HRESIMS, 1D and 2D NMR data, and the absolute configurations were determined on the basis of calculated and experimental electronic circular dichroism (ECD). The antibacterial and antifungal activities of these compounds were tested against Gram-positive—Staphylococcus aureus, Gram-negative—Escherichia coli, and fungal strain—Candida albicans. These compounds showed potential inhibitory effects against S. aureus with minimum inhibitory concentrations ranging from 0.195 to 100 µg/mL.