I am still confused how to follow the singular pronoun "each" by the plural possessive pronoun "their".
Not only these examples I state here, but every day I notice such examples everywhere; in books of Google as well as in many pages, for example, Cambridge.
Here are from Yourdictionary:
Italy’s and France’s economies are improving. (Each country possesses their own economy)
Mark’s and Susan’s dogs don’t get along together. (Each person owns their own dog)
https://www.yourdictionary.com/articles/possessive-nouns
And here is another example from Cambridge :
Each member of the community should take pride in their local environment.