I have been thinking along the same lines of how integration a social platform to existing e-commerce platforms.
You can approach this in different ways, a very tight integration like you are suggesting where their profile page includes their ecomm details, but in reality what benefit does that really bring to the user? Couldn’t a simple link to the ecommerce backend work?
The user account and discourse account should be sych’d I agree, but I would like to understand why you want the order/payment methods on the profile page in discourse?