Input voltage swing when starting a DC brushed motor
Try &quot;holding up&quot; the voltage input to your buck regulator using this method and see if it improves things: -

Also try putting 1 kohm resistors in series with the control lines feeding the H bridge.
You should also ensure that the only connection to your battery negative terminal goes directly to the H-bridge 0 volt connection. The rest of your control circuit and regulators tee-off their ground from the H-bridge 0 volt connection that the battery feeds. This avoids ground bounce.