Pausing application takes a very long time
Open
P2
screen: debugger
- Dominant language
- Dart
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- Avg merge
- 6d 17h
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Description
After clicking pause, it took almost 10 seconds to actually pause the application. Maybe the dart thread was not busy? We should still find a way to pause the app or indicate in the UI that we are trying to pause.

connected app: dart CLI app (web_test)
devtools: profile build on chrome
@elliette
[web-test.zip](https://github.com/flutter/devtools/files/11055378/web-test.zip)
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