Fixes: https://github.com/dart-lang/sdk/issues/26129
The issue was that we were creating the SDK and populating its options (notably `strong-mode`) *before* options processors were called. The result was that client code analysis contexts and SDK contexts were getting configured differently causing confusion when client code was getting analyzed with a non-strong-mode SDK.
BUG=
R=paulberry@google.com
Review URL: https://codereview.chromium.org/1962403002 .
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