Hi everyone. @andypiper here, from the @TwitterDev team.
You can at the moment still create search timelines which will result in a widget ID. For the rest, inside the widget settings on your profile page, you’ll find that we’ve moved to a new “no configuration” model, which means that it is possible to use our publish.twitter.com portal to retrieve the simple embed code you need for collections, user timelines, etc. We are also in the process of moving all of our web embed properties to the publish portal, e.g. buttons etc.
The new model means that there are no “widgets” as such any more - so there are no IDs.
In the past couple of months we’ve rolled out more changes, and it is possible that plugin and other developers should be looking at our oEmbed support for timelines to pull in the data that they were previously picking up the widget ID.
We believe that for the vast majority of use cases and publishers embedding Twitter content, this is a simpler and better experience. We absolutely do hear you if you’re using an alternative third-party solution, and we apologise for the disruption as third parties move over to our newer system. We would love to hear from you about the specific plugins or systems you are using that this disrupts, so that (where possible) we can identify and work with developers to make this better.