Qiskit / qiskit-ibm-runtime / 36679496068

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Ensure that `dag.duration` does not emit non-actionable warning (#3401)

### Summary
Similar to PR #3391, this PR replaces a call to a public attribute of
`DagCircuit` with a call to a private attributes, following the same
path as in Qiskit PR
[#14133](https://github.com/Qiskit/qiskit/commit/d0aa10088)--see
[this
line](https://github.com/Qiskit/qiskit/pull/14133/changes#diff-07e1d3387d241c7d15f4ae9f50051deb7R189),
which happens to be inside the padding pass that our padding pass was
inspired to.

With this, we go from 381 total warnings in our unit tests to 233
warnings, and we address the last of the warnings that is "out of our
control".

### AI/LLM disclosure

- [x] I didn't use LLM tooling, or only used it privately.
- [ ] I used the following tool to help write this PR description:
- [ ] I used the following tool to generate or modify code:

1 of 1 new or added line in 1 file covered. (100.0%)

8673 of 9540 relevant lines covered (90.91%)

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