I have always been told that Heian-Kyo was built with references to the then Tang Dynasty's capital Chang'an, though I often did not see any supporting evidences following such claims. Looking at maps found online, they do share some resemblance in the squares and grids dividing the city, but that sort of layout is not exactly outlandish.
If such modelling did exist, was it an isolated incident only unique to Heian-Kyo, or was it something common during that period of time?
It really was! The "Left" city and the "Right" areas of the city were inspired by how in China the Emperor was flanked by a Minister on his Left and his Right (it is probably that the "Left" and "Right" offices in government were inspired by this same pattern, such as the Great Ministers of the Left and Right, or the Major Controllers of the Left and Right, etc.). Heian-kyo had numerous other similarities to Chang'an as well: Straight avenues that spread across the area in both cities (Ichijo, Sanjo, Rokujo, etc. in Heian-kyo). Both cities had an East and West Market, and both had a square shape.
Emperor Kammu was seemingly bedazzled by Chang'an and other aspects of Chinese culture along with the rest of the court, giving Heian-kyo its striking resemblance to Chang'an.
Sorry if I was rambling, I hope this helped you!