feat: add internal "deadline remaining" client side metric #2341

[djyau]

Thank you for opening a Pull Request! Before submitting your PR, there are a few things you can do to make sure it goes smoothly:

• [ ] Make sure to open an issue as a bug/issue before writing your code! That way we can discuss the change, evaluate designs, and agree on the general idea
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• [ ] All new data plane features have a completed end to end testing plan

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[conventional-commit-lint-gcf[bot]]

🤖 I detect that the PR title and the commit message differ and there's only one commit. To use the PR title for the commit history, you can use Github's automerge feature with squashing, or use automerge label. Good luck human!

-- conventional-commit-lint bot https://conventionalcommits.org/

[mutianf]

/gcbrun

[mutianf]

/gcbrun

[mutianf]

/gcbrun

[mutianf]

/gcbrun