Owen, congratulations on your first foray into using microscope objectives.
Regarding step size, see https://zerenesystems.com/cms/stacker/docs/tables/macromicrodof
for tables that will simplify your estimates. Table 2-C is appropriate for a microscope objective. Your 4X objective is probably NA 0.1, which implies nominal DOF = 0.055 mm. I would typically shoot a little smaller than that, like 0.050 or 0.040 mm, but in no case approaching the 0.005 mm = 5 µm that you used. 0.005 mm step size is typical for a 10X objective.
Objective quality is seldom an issue in the center of the image. Good objectives have flatter fields that retain image quality farther into the corners. But in the center of the field, there is seldom much difference in sharpness between any two objectives that have the same magnification and NA. (NA, Numerical Aperture, is the microscopy equivalent of F-number, except that with NA bigger numbers mean wider aperture, while with F-numbers it's the other way 'round.)
Your image appears soft, but that's probably due to reasons other than lens quality. Unless the subject itself is lacking in sharp detail, softness is probably due to some issue with motion blur.
The most common cause is vibration introduced by mirror slap and/or shutter shock. You are fortunate in that your camera, the Canon EOS 500D, provides an excellent method to avoid those issues. All you have to do is shoot in Live View mode, and then the camera will use what is called EFSC, Electronic First Shutter Curtain, to totally avoid mechanical shock at beginning of exposure. See https://www.robertotoole.com/blog/2014/01/28/electronic-first-shutter-curtain
for an extended discussion. One warning: if you are tethering your camera to a computer, then in some modes the camera will ignore shutter triggers from the rail controller. There is a simple workaround for that; see Step 9 of the recipe at https://zerenesystems.com/cms/stacker/docs/stackshot#canon_t1i_with_canon_eos_utility_software
Another common cause is environmental vibration, for example due to people moving around the room, nearby traffic, nearby motors or fans, and so on. These issues can be exacerbated by any flexibility in the subject mounting. When you're shooting a flower at high magnification, it's best to clip onto it very near the head.
If you still can't get a sharp image, then the next thing to do is to switch to electronic flash illumination, preferably placed close to the subject so that you get nice short "low power" flashes. A flash that's operating at say 1/16 power will typically provide an effective exposure time in the range of 1/5000 second or shorter, which will do an excellent job of freezing out whatever motion blur you might get with a longer exposure.
The last issue I see is that the center of your image has a broad area that appears to be a "hot spot" with reduced saturation and no good blacks. A common cause of that problem is stray light reflecting off the sides of extension tubes. All but the most expensive tubes, and even some of those, will have this problem. Extension tubes almost always need to be flocked or baffled to avoid this problem. A simple solution is to slip a cylinder of flocking paper, or even black construction paper, inside the tubes. The problem can be diagnosed clearly and easily by simply removing the camera and looking into the tube with your eye, placing it where the camera sensor would normally be. See https://www.photomacrography.net/forum/viewtopic.php?t=35350
for discussion and illustrations.
I hope this helps!