Flush logger after running migrations, fix remaining test

[gsoldevila]

Fixes flakiness on:

• Failing test: Jest Integration Tests.src/core/server/integration_tests/saved_objects/migrations/group3 - when migrating to a new version and the mappings' changes are still compatible the migrator skips reindexing #152448
• Failing test: Jest Integration Tests.src/core/server/integration_tests/saved_objects/migrations/group3 - when migrating to a new version and the mappings remain the same the migrator skips reindexing #152472

And also related PR builds failures, e.g. #153332 (failure)

#152818 was a first attempt at fixing this, but I forgot to update one of the tests.

[elasticmachine]

Pinging @elastic/kibana-core (Team:Core)

[kibana-ci]

💚 Build Succeeded

• Buildkite Build
• Commit: f498108

Metrics [docs]

Unknown metric groups

ESLint disabled line counts

id	before	after	diff
securitySolution	433	436	+3

Total ESLint disabled count

id	before	after	diff
securitySolution	513	516	+3

To update your PR or re-run it, just comment with:
@elasticmachine merge upstream

cc @gsoldevila