Syntheses, Structures, and Antimicrobial Activity of New Remarkably Light-Stable and Water-Soluble Tris(pyrazolyl)methanesulfonate Silver(I) Derivatives of N‑Methyl-1,3,5-triaza-7-phosphaadamantane Salt - [mPTA]BF4

Two new silver(I) complexes of formula [Ag(mPTA)4](Tpms)4(BF4) (1) and [Ag(Tpms)(mPTA)](BF4)(2) (mPTA = N-methyl-1,3,5-triaza-7-phosphaadamantane cation, Tpms = tris(pyrazol-1-yl)methanesulfonate anion) have been synthesized and fully characterized by elemental analyses, 1H and 31P{1H} NMR, ESI-MS, and IR spectroscopic techniques. The single-crystal X-ray diffraction study of 1 discloses a noncoordinated nature of the Tpms species, existing as counterions around the highly charged metal center [Ag(mPTA)]5+, 1 being the first reported coordination compound bearing a κ0-Tpms. 1 features high solubility and stability in water (S25 °C ≈ 30 mg·mL−1). The two complexes interact with calf thymus DNA via intercalation mode, binding to the BSA with decrease of its tryptophan fluorescence with a static quenching mechanism. The two new silver complexes exhibit significant antibacterial and antifungal activities screened in vitro against the standard strains of Staphylococcus aureus, Enterococcus faecalis, Pseudomonas aeruginosa, Escherichia coli, and Candida albicans.