Why Geekbench result is three times lower than another result for the same model My MacBook Air (13 inch, mid 2012) started to be very sluggish recently: every action occurs after a visible delay (starting app, loading youtube in a browser, startup, etc). Besides, Newer Tech battery that I installed in mid-December died (macOS thinks I don't have a battery at all).

I ran Geekbench 4 on my machine after closing other apps (I actually left Dropbox and pcloud running, but closed Safari and itunes).
It turned out that my CPU score in Geekbench 4 is three times less than reported by another user with exactly same machine):

https://browser.geekbench.com/v4/cpu/compare/6882608?baseline=6473068

The only difference I can see is that I use macOS 10.13.3 while another user uses macOS 10.13.2.
Can poor performance of my MacBook be attributed only to the difference in macOS version?
No, minor differences in macOS versions do not have an impact of that magnitude on benchmark scores.

If you have battery and thermal problems with the laptop, you might be experiencing performance throttling in order to limit power consumption.