External Media: Allow the MediaUpload component to render a custom button

[Tug]

Is your feature request related to a problem? Please describe.

Yes, in #19628 we enabled external media sources for the story block and noticed the pencil icon in the block toolbar used to edit the story was being replaced with a button with the text Select Media:

Describe the solution you'd like

We'd like to implement a way for blocks to define the button they'd like to use even when there are mutile media sources available. Just like it's already the case for blocks that rely on galleries, we need it for blocks that accept different types of media such as the story block.

The solution could be to reuse the render function and pass it a custom "open" function to detect a click and render the dropdown menu

Describe alternatives you've considered

No real alternatives beside ignoring this issue.