Inline inserter in widget screen needs to be consistent with inline inserter in post editor screen.

[paaljoachim]

Is your feature request related to a problem? Please describe.
I came across this issue: #25800 (comment)
Where it was mentioned the inconsistent treatment of the inline inserter in the widget screen in comparison with the post editor/Gutenberg screen.

In the Gutenberg screen the inline inserter looks like this:

In the widget screen it currently looks like this:

Describe the solution you'd like
We need to add the Browse all button area seen in Gutenberg and add it to the Widget screen inline inserter.