Does anyone know whether the constellation is calculated according to our lunar calendar or work calendar?

It's the Gregorian calendar, which is what we usually call the solar calendar. Because the constellation was introduced from abroad, the Gregorian calendar was used.

Constellation originated in Babylon, one of the four ancient civilizations. 1922. The General Assembly of the International Astronomical Union decided to divide the sky into 88 constellations, and their names basically followed the historical names. 1928, the international astronomical union officially announced the names of 88 constellations. These 88 constellations are divided into three celestial regions, 29 in the northern hemisphere and 47 in the southern hemisphere, near the ecliptic 12.

And the constellation we usually say is the 12 constellation on the ecliptic. Each of them has some myths and legends about himself.