Widget support in Element X

### Your use case

#### What would you like to do?

I want to be able to participate in widgets in EX, and create them via the integration manager.

#### Why would you like to do it?

So I can use things like neoboard

#### How would you like to achieve it?

Implement the widget API.

### Have you considered any alternatives?

_No response_

### Additional context

Totally failing to find an existing issue for this.

Start by locating the Element X integration manager and any existing widget API entry points. Compare the required participation and creation flows with the neoboard use case, then define the supported API surface and tests needed to demonstrate both flows work.

Written by the indexing model from the issue text.