Nikon Z50 has a
21.0MP APS-C (23.5 x 15.7 mm ) sized BSI-CMOS sensor and features Expeed 6 processor. On the other hand, Sony A77 II has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz X processor.
Another difference between these two cameras is that Nikon Z50's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the Z50 and A77 II sensor size comparison.
Nikon Z50 and Sony A77 II have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.