I think the confusion comes from footnotes like
5 V tolerant pad providing digital I/O functions with TTL levels and hysteresis. This pin is pulled up to a voltage level of 2.3 V to 2.6 V.
And no, I don't know what they mean with this. Esp. if this applies to input or output configuration.
Section 14.4 in the datasheet shows the typical I/O pin configuration. They have no special 5 V output provisions. Which is not surprising, because they have no 5V generator on the chip.
So what I understand is that you can just use the pins in two common output configurations, normal push-pull or open-drain. In normal configuration you get a minimum of Vdd - 0.4 V, aka. 2.9V high level at 4 mA. That is good enough for the TB6560. If you check section 10.3, the 100K pull down should not be a problem.
In open-drain output mode you need an external pullup to pull the pin to 5V. It needs to be stronger than theTB6560s internal 100K pulldown. This would give you more wiggle room when looking at the required 2 V minimum high for the TB6560.