I am curious why there is not a cross on top of this old church and what is that thing they have instead? https://www.thebyzantinelegacy.com/koimesis-nicaea
I can't be completely sure due to the quality of the photo and the angle it has been taken from, but the symbol you are referring to looks like the Orthodox Golgotha Cross. It was generally depicted as the eight-pointed cross (i.e. with an additional bar above the main one and slanted one below) or, in some cases six-pointed cross (i.e. with only the slanted bar added), additionally adorned with the depiction of the two items used in the Crucifixion, namely the spear used to pierce Christ's side, traditionally portrayed on the left and a sponge on a pole used to give vinegar to the Christ, portrayed on the right (the form differs - it can be a circle, rectangle, cylinder, star or even a shape resembling sausage on a stick). As the location of the spear and sponge is generally constant, one can assume that the picture of the dome and cross near the end of the article has been taken from the front of the church. Depending on the type of depiction, these two implements might be positioned at an angle, optionally crossing the horizontal bar (like in portrayed example) or vertically, especially if they adorn cross meant to be worn.
When used on the robes, banners or the similar items, this cross is commonly adorned by additional symbols, such as steps at the bottom of the cross, symbolizing the Golgotha mountain, 'Adam's head' (i.e. skull and crossbones), angels, cockerel, items used to crucify Christ (ladder, hammer, nails) and various abbreviations, such as IS CHR (Jesus Christ), NIKA (gr. 'victory'), SN' BZh' (Son of God), TsR SLV' (King of Glory) etc. You can see such depiction of the cross on this analav worn by the Orthodox monks of strict closure (this particular specimen is located on the exhibition in Suzdal Kremlin).
Golgotha Cross has been quite commonly used in various contexts in the Eastern Orthodox Christian areas, often used not only as the symbolic adornment of the church and liturgical robes, but also as the common symbol on the military flags, along the simple Orthodox cross, Adam's head and religious slogans or quotes from the Bible, especially in 17th and 18th century, although since 19th century its usage was gradually limited and now it is used almost solely in the monastic context.