<p>Got my Ender 3 v2 and stack with the bed leveling.</p>
<p>Used default settings, Creality slicer 4.2, test PLA from the kit and print model <a href="https://www.thingiverse.com/thing:3013319" rel="nofollow noreferrer">https://www.thingiverse.com/thing:3013319</a> (4 squares in each corner and 1 in the middle), nozzle 200 °C, bed 60 °C.</p>
<p>After some adjustments, I have good solid pieces on the bed corners  but the center one has small gaps. Is it possible to fix this problem?</p>
<p>Corner pice:
<a href="https://i.stack.imgur.com/BGeA2.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/BGeA2.jpg" alt="enter image description here" /></a></p>
<p>Center piece:
<a href="https://i.stack.imgur.com/gfSas.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/gfSas.jpg" alt="enter image description here" /></a></p>

The gaps are, because the nozzle is to far from the bed at this point. It may sound like a big deal, but actually this is not leveling alone, but it looks like the bed is not a perfect plane/perfectly flat. This is normal, my ikea mirror and my stock bed show the same thing. Now here's one solution:
Print calibration stickers, like you already did on various places around the bed to get a feel, where it is too low. Let it cool and put painters tape (the very very thin tape, that should not burn) on areas, where the bed is too low. Print more calibration rectangles and check if you have enough. Repeat until you cannot see a difference.
It took me about 2h to level everything absolutely perfectly. This was 2 years ago and I didn't have to touch the tape below my bed ever since. It just works.
Alternative solutions involve mesh bed leveling and buying a new bed surface or even the surface below the bed. However, I found that to neither of them work reliably, whereas the simple tuning does what it's supposed to.