Fix [rustdoc] Non-json time diagnostics in stdout when using --format…

[cp90-pixel]

I've updated the display_times method in doctest.rs to check if JSON output is requested before printing the timing information. Here's what the change does:

Added a check for --format or --format=json in the command-line arguments using std::env::args().any()
The timing information will only be printed if:
There were merged doctests compiled (self.added_compilation_times > 0)
AND JSON format is NOT requested
This change ensures that when running with --format json, the timing information won't be printed to stdout, which would otherwise corrupt the JSON output. The timing information is still available when running in the default format.

[rustbot]

r? @GuillaumeGomez

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[GuillaumeGomez]

Not displaying in JSON output format is not a fix. ^^'

[GuillaumeGomez]

Related issue: #144798

The correct fix would be to display the output in the expected format, not display it only when not JSON. Also I assigned this issue to me as it might be a bit more complex than that.

[rust-log-analyzer]

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##[endgroup]
[TIMING] core::build_steps::tool::ToolBuild { build_compiler: Compiler { stage: 0, host: x86_64-unknown-linux-gnu, forced_compiler: false }, target: x86_64-unknown-linux-gnu, tool: "tidy", path: "src/tools/tidy", mode: ToolBootstrap, source_type: InTree, extra_features: [], allow_features: "", cargo_args: [], artifact_kind: Binary } -- 11.285
[TIMING] core::build_steps::tool::Tidy { compiler: Compiler { stage: 0, host: x86_64-unknown-linux-gnu, forced_compiler: false }, target: x86_64-unknown-linux-gnu } -- 0.000
fmt check
Diff in /checkout/src/librustdoc/doctest.rs:65:
         // displayed by `libtest` for standalone tests are already accurate (they include both
         // compilation and runtime).
         // Skip output if JSON format is requested to maintain valid JSON output.