Refactor the App Check internal call logic used by other products

[a-maurice]

Description

Provide details of the change, and generalize the change in the PR title above.

Change the internal call logic to return the token as just a string, instead of the struct. This prevents the need for the products using the function registry to include the App Check header for the struct definition. Also, use a new future, instead of reusing the public one, which might have lead to confusion with the LastResult functionality.

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Testing

Describe how you've tested these changes. Link any manually triggered Integration tests or CPP binary SDK Packaging Github Action workflows, if applicable.

Local testing of the desktop implementation.

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Type of Change

Place an x the applicable box:

• Bug fix. Add the issue # below if applicable.
• New feature. A non-breaking change which adds functionality.
• Other, such as a build process or documentation change.

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Notes

• Bug fixes and feature changes require an update to the Release Notes section of release_build_files/readme.md.
• Read the contribution guidelines CONTRIBUTING.md.
• Changes to the public API require an internal API review. If you'd like to help us make Firebase APIs better, please propose your change in a feature request so that we can discuss it together.

[github-actions]

❌  Integration test FAILED

Requested by @a-maurice on commit 6bf9316
Last updated: Tue Feb 28 20:47 PST 2023
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Failures	Configs
missing_log	[TEST] [ERROR] [Android] [All 3 os] [1/2 android_device: android_target]
storage	[TEST] [ERROR] [Windows] [x64] [openssl]

Add flaky tests to go/fpl-cpp-flake-tracker