I didn't measure, but perhaps a little under 1 ft. Nikon says .9 ft min focus distance. Of course that is from the focal plane, so distance from the front of the lens is less. If you want to maximize your magnification, put it on 55mm. If you are using AF, half press the shutter and wait for the focus confirmation beep. Move in until it will no longer confirm, then back out until you get the beep. Keep in mind that with extension tubes you will loose some light. This may cause your AF to struggle more to capture focus. I don't know how much you would lose, perhaps 1 stop? If you are using the 55mm setting on your zoom it's already at F5.6, so that would end up F8, and you are likely getting into borderline territory for the AF. Of course, you could zoom out to a shorter focal length which would give you more light wide open. It looks like you gain that stop back at somewhere around 28mm. Ironically, this will also give you more magnification than at 55mm, but you will have to move in closer to the subject. That's one reason that macro lenses in the 100 mm range are popular. They give more working room between the lens and subject. Using shorter tube(s) will also give more light, at the expense of less magnification.
The Z 105 micro is a very sharp lens, IMO. The FX 105 micro is also a very good lens and should give similar results, although the Z lenses are regarded to be somewhat sharper due to the larger mount. Also, the picture shown was shot on my new Z7ii, which has a 45 MP sensor. That makes a difference when cropping compared to a 24 MP sensor. The 24 MP sensor will definitely do the job, you just may not be able to crop as deeply, or make as big an enlargement.
Last year, I took a number of pictures using extension tubes and my Z 24-70 F4 lens. You would be hard pressed to tell which were taken with that, and which were taken with the 105. I notice a difference when cropping, or blowing up sections to check for sharpness, but looking at normal enlargements they compare well. If you are doing a heavy crop, it can make a difference. The biggest issue I had with the extension tubes was the lens being too close to the subject for my tastes. At $360 -$385 for an "excellent" condition used FX 105, you can't go wrong, IF you can afford it, and IF you have enough interest in macro photography. The extension tubes are a great way to discover if you have the interest.
Do you have an external flash?