Workaround race condition in ShutdownAPI and logging and custom mem mngmt

[SergeyRyabinin]

Issue #, if available:
TEST(AwsMemoryManagementTest, MultiInitParallel) fails once in a blue moon with sanitizer report in case of custom memory management enabled.
It is not an issue in case of basic-use non-violated.
We really need to refactor the InitAPI-ShutdownAPI design...
Description of changes:
Preserve the logger for some time to let all pending logging statements to finish.
This is a workaround not a real fix.
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• Did a review by yourself.
• Added proper tests to cover this PR. (If tests are not applicable, explain.)
• Checked if this PR is a breaking (APIs have been changed) change.
• Checked if this PR will not introduce cross-platform inconsistent behavior.
• Checked if this PR would require a ReadMe/Wiki update.

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