Serialization for diff and profile tabs.

[polina-c]

[polina-c]

Please add tests for the new serialization and any other affected code as part of this change.

Added tests for serialization. Most of other code is test covered.

I will add more coverage after completing the feature and before removing the flag.

[auto-submit[bot]]

auto label is removed for flutter/devtools/7699, due to - The status or check suite devtools_shared test has failed. Please fix the issues identified (or deflake) before re-applying this label.

[auto-submit[bot]]

auto label is removed for flutter/devtools/7699, due to - The status or check suite devtools_app integration-test integration_dart2js - flutter - shard 2/3 has failed. Please fix the issues identified (or deflake) before re-applying this label.