Changing lenses on any given camera won't change your depth of field as stated above the DOF is set by magnification on the sensor and aperture - as you put on higher magnification the DOF decreases. If you look at a DOF calulator is shows that at f22 and 30cm distance and 50mm focal length you should have 25mm DOF. But you are using close up lenses to get more magnification which will reduce your depth of field. You can also find online calculators to estimate magnification with diopters and your setup will give you about 0.7x magnification at min focus and +6 diopter.
So with your bare lens you get about 0.27x magnification and 25mm DOF. Put on a 0.6x diopter maginifcation jumps to 0.7x and DOF plummets to around 3mm.
Now change to f10 and your DOF is 8mm with bare lens and 1.4mm with the +6, both at their maximum magnification. Both magnification and focal length influence DOF as they change the magnification.
So you can see the difference between 1.4 and 3mm is not that much so hard to see anything in your photo, but backing off a little to reduce magnification will have a bigger impact on DOF. This is exactly what is happening with the Olympus TG4/5, because the sensor is so much smaller the magnification required to fill the frame is less so the depth of field increases. Add to this the short focal lengths they use on the small sensor to keep magnification low allows the lens to be designed to focus really close. So to get more depth of field back off a little and crop the photo or use a lower power diopter.
Another thing to consider is how you place the depth of field, if you focus on the tip of a nudi's nose with 3mm DOF, then the area in focus is 1.5mm either side of the the focus point. In this case it looks like you only have 1.5mm DOF as the 1.5mm in front of the subject is water and the DOF is "wasted" . Better to focus on the rhinopores and have 1.5mm in focus either side of them. You need to decide what is important to be in focus and focus on that, and consider the subject orientation as well - front on/side on/at an angle etc.