[core] Improve traversal context in inspect_serializability

[prince8273]

Summary

Improve serialization debugging by propagating traversal ancestry/path context during recursive serialization inspection.

Problem

Current diagnostics only preserve immediate parent context, making localization difficult for nested object graphs and closures.

Solution

Track traversal paths during recursive inspection while preserving all existing behavior.

Example Improvement

Before: FailTuple(lock [obj=<lock>, parent=<Pipeline>])
After: FailTuple(lock [path=train -> model -> pipeline -> executor -> lock, obj=<lock>, parent=<Pipeline>])

Non-goals

• No serialization behavior changes
• No traversal algorithm redesign
• No cloudpickle modifications

Tests

Added regression coverage for nested objects, closures, and path propagation.

[gemini-code-assist]

Code Review

This pull request enhances the serialization inspection utility by replacing the single 'name' attribute with a full traversal 'path' in FailureTuple, allowing for better debugging of serialization failures. It includes updates to the inspection functions to propagate this path and adds corresponding test cases. Feedback highlights a critical issue in the path initialization logic that leads to name duplication and a potential TypeError when the object name is None.

[cursor]

Cursor Bugbot has reviewed your changes and found 1 potential issue.

^{Reviewed by Cursor Bugbot for commit 826ac2f81ce1d5d483c1063142486757b41aaab6. Configure here.}

[prince8273]

@edoakes
The test_object_summary_aggregator failure appears unrelated to this PR's changes (which only touch check_serialize.py). This test has no overlap with path tracking in inspect_serializability. Requesting a re-run of the affected shard.