fix(timing)!: remove --timings=<FMT> optional format values

[weihanglo]

What does this PR try to resolve?

Arguments to remove it

• The --timings=json is obsolete as -Zbuild-analysis logging is
  a more approachable option, which doesn't need passing
  --timings=json ahead of time.
• There is no support infra built around --timings=json yet,
  while for -Zbuild-analysis we have cargo report timings already.
• --timings=json is a UI feature inherently unstable, and has no tests.

Counterargument:

• --timings=json outputs to stdout, but there is no alternative yet
  also outputs to stdout.
  feat(log): add output control #16418 was an attempt to add that back,
  but we then decide to punt until seeing requests or needs.

How to test and review this PR?

• cargo help build and check the manpage
• cargo build --help and cehck the help text
• cargo build --timings and it works

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[weihanglo]

Does it require an FCP?

[epage]

Might be good to get a vibe check in case there is interest in build analysis having X amount of functionality before it can replace --timings=json

[weihanglo]

This has entered FCP: #16420 (comment).

I personally don't think we need to wait for the extra 10 days.

• People may not notice the removal until at least it hits nightly.
• People care about the evolution of timing report may have already followed the goal update in https://blog.rust-lang.org/2026/01/05/project-goals-2025-december-update/
• This is a nightly feature.

I am fine if we still want to wait for the full FCP.

[weihanglo]

@rfcbot fcp merge T-cargo

This removes support for --timings=json, making --timings a plain boolean flag after JSON timing output was removed. See the PR descriptions for more.

[rust-rfcbot]

Team member @weihanglo has proposed to merge this. The next step is review by the rest of the tagged team members:

• @0xPoe
• @Eh2406
• @Muscraft
• @arlosi
• @ehuss
• @epage
• @joshtriplett
• @weihanglo

No concerns currently listed.

Once a majority of reviewers approve (and at most 2 approvals are outstanding), this will enter its final comment period. If you spot a major issue that hasn't been raised at any point in this process, please speak up!

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[rust-rfcbot]

🔔 This is now entering its final comment period, as per the review above. 🔔