I had 240gal system years ago with external pumps and yes they were generating heat, so I eventually changed to DC pump with lower wattage. Your pump is rated 400-500w, additionally you are running water through long pipes which also generate some heat due to friction. How much does it contribute to increasing your tank temp is uncertain though.
The heat generated in the piping is minimal. A watt is a watt, so all 400W ends up as heat in the room or the tank one way or the other. Be it "friction" in the piping or literal water movement in the tank. You can't cheat the physics.
Your DC pump of lower wattage produced lower heat.
Abyzz is a DC pump with lower wattage than corresponding AC pumps, so it's worth while considering as it would save you some bucks on electricity bill.
AC induction (PSC) motors lose some efficiency due to slip, rotor losses, and bearing friction, but they use line voltage and frequency directly, with no conversion losses.
Also, this is a residential setting and residential meters measure real power (watts), not reactive power, so you aren’t billed for the power factor component. If these were giant industrial pumps at a factory, then the lagging power factor losses would play a role.
Brushless DC pumps can achieve slightly higher motor efficiency through better electronic phase control, but they incur conversion losses in both the AC to DC power supply and the inverter transistors that generate the three phase output to the motor. For hobby grade equipment, these losses are easily 10%-20% or more. For commercial equipment, they may be lower than 10%. I think you will find that Abyzz has had some issues with power supply and driver heating issues, but I don't know their overall efficiency.
While a BLDC motor and controller typically run at unity power factor, the PF savings only comes into play with large industrial customer.
BLDC pumps are attractive for several reasons, but mostly because they don't lose efficiency when speed controlled. So BEP (Best Operating Point) is not a fixed point like it is with a PSC drive pump.
So in the end, there are not great electric or heat savings for most users who switch to DC pumps, unless of course they are moving less water. To that end, many of the flow ratings on pumps sold to this hobby are ridiculously inflated.