Definition of header timestamp

[YuqiHuai]

Given a module starts execution at t0, finishes execution at t1, and produces an output with header timestamp x, what is the value of x?

If the definition of header timestamp indicates when the output is being produced, then x == t1 should always be true. For example, in the following code snippet
https://github.com/autowarefoundation/autoware.universe/blob/edd5824b01fbc3e6d5eebfb15f50da9af95f1cba/planning/behavior_path_planner/src/behavior_path_planner_node.cpp#L692-L717
output.header.stamp seems to consider the processing time of motion_utils::convertToPath.

In a different function https://github.com/autowarefoundation/autoware.universe/blob/edd5824b01fbc3e6d5eebfb15f50da9af95f1cba/planning/behavior_path_planner/src/behavior_path_planner_node.cpp#L719, header timestamp is assigned once, and seems like the same value may be used again at https://github.com/autowarefoundation/autoware.universe/blob/edd5824b01fbc3e6d5eebfb15f50da9af95f1cba/planning/behavior_path_planner/src/behavior_path_planner_node.cpp#L438C34-L438C38. Assigning header timestamp only once at an early stage ignores the processing needed, therefore x may be some value between t0 and t1 (actually closer to t0 since it is assigned at an early stage).

I am not seeing any issues at the moment, but from a design perspective, will there be any benefit in strictly defining what header timestamp refers to and fixing any inconsistencies that are currently implemented?