Are soft-sided coolers actually leakproof?

Only some are. Among the picks here, YETI's Hopper Flip line and the CleverMade Pacifica are explicitly marketed and reviewed as leakproof with welded or sealed seams. Cheaper insulated tote bags like the Jumbo Insulated Cooler Bag are not truly leakproof and will weep if ice melts fully. Look for welded seams, a waterproof zipper or roll-top, and a TPU or PVC liner.