How to create a block of links shared by a user?
Just wanted to make sure you've tried this simple approach. Create a check-box field for the all posts (whatever content-type it is) you were referring to with options embedded or non-embedded and create a view with a filter to only display embedded content.

Edit: Have a checkbox for the content-type (responsible for posts) which asks anyone creating posts if they are using the oembed text filter, give a description to check "embedded content" if they are.
Then create a view and pull all the posts by setting the filter- "CheckboxName (isOneOf) Embedded content".