Refactors `try` to avoid `unawaited_return_in_try_block` case (#191129)

This merely refactors a `try`, so it works as expected by the authors.
I'm not sure why the bot didn't trigger this case along with
https://github.com/flutter/flutter/pull/188910.

Still work towards:

- https://github.com/dart-lang/sdk/issues/62555.

We are now making the new `analyzer` warning trigger on non-`async`
cases too because that is probably what the code is _meant_ to do.

I don't expect this change to break any tests. If it does, we caught an
untracked error.

CC @navaronbracke

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Co-authored-by: Mohellebi Abdessalem <116356835+AbdeMohlbi@users.noreply.github.com>