The micrometers per pixel does not change the actual image resolution unless the resolution was previously limited by the camera rather than by the optical system.
The OpenFlexure high resolution optics modules, using microscope objectives and a Pi Camera 2, are limited by the optical resolution of the objective lenses. We have not tried the Pi HQ camera, although a couple of people on this forum have. It is a little tricky to design a high resolution system with the HQ camera that is physically short enough to fit in the microscope sensibly. With an appropriate optical system the HQ camera will also give images limited by the optical resolution of the objective lenses. So that will be the same as for the Pi Camera 2.
Where the HQ camera could be a benefit in microscopy is the sensitivity and noise levels, which might be better for the larger sensor. In normal photography the noise reduces with increasing size of the sensor, because to get the same field of view you need a longer focal length lens, and at the same f# (or NA in microscopy) the lens is then a larger physical diameter and collects more light. I am not sure that this argument translates into microscopy where we are using the same objective lens, so collecting the same amount of light but then imaging it onto a bigger sensor.