After some digging, I found that the Amazon app is sharing "text" type instead of a link since they are trying to include the name of the item and other information. Therefore, I can have my app be an option by including the following in my Info.plist:

<key>NSExtensionActivationSupportsText</key>
<true/>

However, it should be noted that I'll now need to parse what is coming in to find the URL since it is embedded among other items.