Improve flat storage tests coverage

[exalate-issue-sync]

Plan:

• Update test_save_to_file to also check for the flat storage data
• Proper deletion of FlatStateDeltas #8655
• Make flat storage creator compatible with state sync #8250
• Fix of issue raised by Jakob fix: more precise flat storage errors #8740

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First ideas of what we should do:

• Uncomment and fix test_state_sync currently marked with #[cfg(not(feature = "protocol_feature_flat_state"))]
• Introduce FlatStorageCreationStatus::SyncingState when we sync flat storage state for given shard during state sync or catchup. Use it to crash if we attempt to initiate background migration, and vice versa - if we attempt to sync flat storage when background migration didn't end.
• If background migration is running but the block for which we create it got GC-d (see Chain.clear_data), we should interrupt node

[Longarithm]

When we attempted to implement debug tool and add support for params-estimator, there was several notable design challenges discovered. This resulted in several discussions on how we could design better API for flat storage and cleanup the code after we implemented prototype. Anton started working on it and created an issue #8577

[Longarithm]

See #8577 for more granular progress.
#8664 which splits flat storage into multiple files was merged today.

[Longarithm]

Strictly speaking, we don't have 100% progress here, because #8577 had more priority and was much more complex.
Still we implemented some tests, so I dump remaining issues to the newly created #8826 and close this one.