[core][Android] Make defaultAppContextMock private

[lukmccall]

Why

An improved version of the fixed proposed here: #28601.

How

To simplify our test setups, we should use the same set of mocks for each test case. Currently, we are using different mocks to start our tests in a few places, which is not scalable. Therefore, I suggest using a universal entry point to replace it.

Test Plan

• unit tests ✅

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The Pull Request introduced fingerprint changes against the base commit: 2d80ee3

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