At what point a battery becomes a load
The answer is simply \$ V_{PSU} &gt; V_{batt} \$.

When this is true power will flow from the power supply to the battery.

When \$ V_{PSU} &lt; V_{batt} \$ then the battery will take over. Whether current flows from the battery into the power supply depends on the PSU design. Generally it will not as the output diodes prevent it.

Where PSU and batteries are connected care has to be taken in the design to prevent over-voltage and over-current conditions which may damage, destroy or explode the batteries.