I'm replacing my carpeted stairs with 1/2" engineer hardwood to match the flooring on the first and second floors. After removing the carpet, I see that the current risers and treads are 5/8" CDX plywood, which is the subfloor on the second floor.

On the second floor, I stapled a sheet of 3/8" plywood on top of the subfloor, prior to installing the flooring.

For the stair treads, should I replace the 5/8" plywood tread with 3/4" plywood or add a piece of 3/8" plywood over the existing tread?

For the stair risers, should I replace the 5/8" plywood riser with 3/4" poplar or add a piece of 1/2" poplar in front of the existing plywood riser?

(Also, what's recommended for riser material - poplar or MDF - it will be painted.)

You could add 3/8th plywood to the treads and keep to within tolerance so all treads are within 3/8ths inch including top and bottom tread heights, which is the code. This is the goal, for safety.
You could add either poplar or mdf for the riser material. The ends of the risers can be covered with brackets that die into the tread returns.The MDF will paint well if you prime the cut ends well. You can get primed MDF.