Fix doctest output json

[GuillaumeGomez]

Fixes #144798.

Hopefully it will work with the new changes in libtest without needing to do both at once.

This PR moves the rustdoc merged doctest extra information directly into libtest to ensure they share the same rendering to prevent the bug uncovered in #144798.

cc @lolbinary (as you reviewed the first PR)

And since we're making changes to libtest:

r? @Amanieu

[GuillaumeGomez]

This is very frustrating that libtest cannot be used like any other dependency. Is there a reason to that @Kobzol ?

[Kobzol]

Well, that is kind one of the outputs of the stage0 redesign. cfg(bootstrap) has moved from the stdlib to the compiler (so rustc and rustdoc). If you need to use new unstable library APIs (which includes libtest) in rustc/rustdoc, you have to support both stage0 and stage1 with cfg(bootstrap) until beta is bumped.

[GuillaumeGomez]

Like usual, I will wait for the separate PR I opened to be merged and available.

[lolbinarycat]

We could just decide stage 1 rustdoc shouldn't exist, though that would mean that testing rustdoc would be slightly more work if you're not using download-rustc, since you could no longer just run the tests against stage1 rustdoc to prevent an extra rebuild of rustc (useful when making changes to compiler queries only used by rustdoc)

[GuillaumeGomez]

I'd rather not. ^^'

Once upon a time, changing libtest worked fine with rustdoc stage 1. Not sure when and why it changed, makes things more convoluted.

[Kobzol]

It changed with the stage0 redesign. Before building in-tree libstd was required to build rustc, but not anymore (https://blog.rust-lang.org/inside-rust/2025/05/29/redesigning-the-initial-bootstrap-sequence/).

[rust-log-analyzer]

The job pr-check-2 failed! Check out the build log: (web) (plain enhanced) (plain)

Click to see the possible cause of the failure (guessed by this bot)

[RUSTC-TIMING] askama test:false 0.189
error[E0425]: cannot find function `print_merged_doctests_times` in crate `test`
   --> src/librustdoc/doctest.rs:398:23
    |
398 |                 test::print_merged_doctests_times(&test_args, total_time, compilation_time);
    |                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^ not found in `test`

error[E0425]: cannot find function `print_merged_doctests_times` in crate `test`
   --> src/librustdoc/doctest.rs:406:15
    |
406 |         test::print_merged_doctests_times(&test_args, total_time, compilation_time);
    |               ^^^^^^^^^^^^^^^^^^^^^^^^^^^ not found in `test`

For more information about this error, try `rustc --explain E0425`.
[RUSTC-TIMING] rustdoc test:false 3.634
error: could not compile `rustdoc` (lib) due to 2 previous errors

[bors]

☔ The latest upstream changes (presumably #145210) made this pull request unmergeable. Please resolve the merge conflicts.