Driving high current through an LED using PWM
4 microseconds is not a lot of time, so the parasitic inductance and capacitance could be a problem.
It is impossible to tell from the current schematics, but if you have an oscilloscope, you need to:

Measure the voltage on the transistor's base. What is the rise time there? If it is too long, then maybe your IC's output is not powerful enough, or you have a parasitic capacitance in that circuit.

Measure the voltage on the transistor's collector. It should have a fast rise as well. If it does not, then you have too much capacitance on the input.

You can also measure the current on Rc to see if there is a problem with parasitic inductance -- but this is pretty unlikely unless your LED is on the very long wire.