build: move typings_test to new integration test fixture

[alexeagle]

Please check if the PR fulfills these requirements

• The commit message follows our guidelines: https://github.com/angular/angular/blob/master/CONTRIBUTING.md#commit
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

What kind of change does this PR introduce? (check one with "x")

[ ] Bugfix
[ ] Feature
[ ] Code style update (formatting, local variables)
[X] Refactoring (no functional changes, no api changes)
[ ] Build related changes
[ ] CI related changes
[ ] Other... Please describe:

What is the current behavior? (You can also link to an open issue here)

behavior is unchanged - pure refactoring

Does this PR introduce a breaking change? (check one with "x")

[ ] Yes
[X] No

If this PR contains a breaking change, please describe the impact and migration path for existing applications: ...

Other information:

[alexeagle]

note @chuckjaz this has your #14124 included here

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