The TPSV687M006R0050: The 50 mOhm ESR keeps ripple heating under control in power-supply output filters and point-of-load decoupling — the capacitor dissipates less heat per amp of ripple current than a higher-ESR part, which matters when the board runs near the 125 °C ceiling.
Temperature range and package — board-fit constraints
Surface-mount assembly with ±20 % tolerance on the 680 µF nominal; the tolerance band is standard for tantalum electrolytics and is accounted for in the output ripple budget during design.