Regular soap does also kill bacteria with those hydrophobic sides of its molecules by breaking a bacteria or virus’ lipid membrane. I would argue this still a mechanical process though. Antibacterial soaps use a specific chemical, Triclosan, that binds with enzymes within the bacteria that prevent it from reproducing.
Outside of antibacterial or germicidal soaps, the cleaning action of washing with soap is 100% mechanical. Soap molecules are asymmetrical and have one side that’s hydrophilic and one side that’s hydrophobic which, when used with water, creates a nifty mechanism that picks up crap on one side and catches a ride on the water molecules with the other side.