L298N minimum output current/voltage
The L298N has two H-bridges in it, which are either connected to Vcc or ground (depending on what the input is).
The minimum voltage is ViH+2.5V. The minimum ViH voltage is 2.3. So the minimum output voltage would be 4.8V for Vcc.
When switched low the bridge will be slightly above ground because of the transistors, which will be the saturation voltage found in figure 1. This voltage is dependent on the current and won't go to zero because of the voltage across the low side transistor. So yeah you should be measuring a small voltage across the load on the out pin.

Source: https://www.st.com/content/ccc/resource/technical/document/datasheet/82/cc/3f/39/0a/29/4d/f0/CD00000240.pdf/files/CD00000240.pdf/jcr:content/translations/en.CD00000240.pdf