Change traverse implemention to in-order traverse

[qiuchengxuan]

the current traverse implemention has several weakness:

1. unable to stop traverse, thus unable to reduce traverse time
   complexity around O(logN)
2. out-of-order, ordinary traverse method should be pre-order, in-order,
   post-order, but the current implemention belongs none of them
3. memory cost, since traversing in flat levels, maximum memory usage
   will reach to nearly half tree width

[aviary2-wf]

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Action Items

• Review PR for security impact; comment "security review required" if needed or unsure
• Verify aviary.yaml coverage of security relevant code

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