Just adding a suggestion here, in case other companies also can see a benefit from this;

It would be nice to have more contact details visible in the contact tab of a product (see image below). This could be used to quickly sort between the different contacts associated with a product.

For instance, you could have a custom field for contacts that determine what kind of contact it is: for example "Supplier" or "Product owner". If this custom field could then be made visible in the contact tab of the product, you can instantly see which contact in the list is of interest to you in your current case and which aren't.

Perhaps the same idea could be applied to the "Contacts" section for an account.