Allow to disable console output in dev tools

## Use case

My application uses plenty of logging during development. These are not just `print` statements but output from `logger` package. It's not unusual at some point that there will be 100s of lines printed to STDOUT, for example when my Flutter application is making network requests (I print out serialized responses).

Of course most of this is disabled for production builds. However when debugging my application this output causes the dev tools to freeze as it's trying to catch up and print everything to the console below.

## Proposal

I think ideal solution would be to improve performance of the web application (devtools). But I guess that might be tricky so at least allow me to:

1. Surpress messages to console completely (I already have output in my terminal where `flutter run` process is launched).
2. Allow me to close console pane completely and ignore any messages.

No files or tests are named. Start by locating the DevTools console pane and tracing how application log messages reach it. Done means users can suppress console messages or close the pane so output is ignored without the DevTools UI freezing.

Written by the indexing model from the issue text.