[ci][web] Run integration tests in wasm.

[ditman]

This PR runs the integration tests in web packages using Wasm.

(This should fail, because packages need a further migration review like this one)

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene page, which explains my responsibilities.
• I read and followed the relevant style guides and ran the auto-formatter. (Unlike the flutter/flutter repo, the flutter/packages repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the package surrounded by square brackets, e.g. [shared_preferences]
• I linked to at least one issue that this PR fixes in the description above.
• I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or this PR is exempt from version changes.
• I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style, or this PR is exempt from CHANGELOG changes.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or this PR is test-exempt.
• All existing and new tests are passing.

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