[Dart] Make clients crossplatform

Created by: nickmeinhold

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• Ran the shell script under ./bin/ to update Petstore sample so that CIs can verify the change. (For instance, only need to run ./bin/{LANG}-petstore.sh, ./bin/openapi3/{LANG}-petstore.sh if updating the {LANG} (e.g. php, ruby, python, etc) code generator or {LANG} client's mustache templates). Windows batch files can be found in .\bin\windows\. If contributing template-only or documentation-only changes which will change sample output, be sure to build the project first.
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Description of the PR

Since 12.0 the http package has had conditional imports so creating a Client() will use the appropriate option of either a BrowserClient or an IOClient depending on the platform so there would seem to be no need for the generator to use a browserClient flag to distinguish between Flutter and the web.

I didn't create an issue as there was already #3540 (closed) (although it's been closed so I wasn't sure what I should do).