How to sync colours for contacts in different apps?

[AC Question]

I like the way Gmail and Messenger are using colour to distinct various contacts. (I rarely use pictures for my contacts, so the colours are very visible)

But most of my contacts now have three different colours: one in Gmail, another one in Messenger and yet another one in Contacts. This is not logical and confusing.

I know there is a way to change contact colour in Messenger. But is there a way to sync colour on Contacts level?

If there is, I haven't found it yet.
Any ideas?

Thanks!