Current sinking with PC13 on STM32F103C8T6
No it is not.

Reasoning:

The LED is connected to 3.3 V, is a blue LED and has a current limiting resistor of 510 ohm.

Blue LEDs have a forward voltage drop of around 2 V (this is a low value estimate for low currents, it's likely higher), so 1.3 V left for the resistor, gives a current of around 2.5 mA.

I'd say it's fine. Maybe a bit borderline as the forward voltage drop of LEDs is not a very well specified value, but should be okay.