rustdoc `--persist-doctests` does not work with `--test-run-directory`

[ehuss]

The combination of --persist-doctests doesn't seem to work with --test-run-directory.

Reproduction:

1. mkdir foo

2. cd foo

3. mkdir subdir

4. Create subdir/example.rs with the contents:

   /// ```
   /// example::foo();
   /// ```
   pub fn foo() {}

5. rustc --crate-type=rlib subdir/example.rs

6. Verify a basic test works: rustdoc --edition=2021 -L . --test subdir/example.rs

7. Verify that persist-doctests works: rustdoc --edition=2021 -L . --test subdir/example.rs --persist-doctests persist -Zunstable-options

8. Verify that test-run-directory works: rustdoc --edition=2021 -L . --test subdir/example.rs --test-run-directory=subdir

9. Check behavior when both are specified: rustdoc --edition=2021 -L . --test subdir/example.rs --test-run-directory=subdir --persist-doctests persist -Zunstable-options

Expected behavior: Tests should run successfully.

Actual behavior: Test fails with this error:

running 1 test
test subdir/example.rs - foo (line 1) ... FAILED

failures:

---- subdir/example.rs - foo (line 1) stdout ----
Couldn't run the test: No such file or directory (os error 2)

failures:
    subdir/example.rs - foo (line 1)

test result: FAILED. 0 passed; 1 failed; 0 ignored; 0 measured; 0 filtered out; finished in 0.06s

Meta

rustc --version --verbose:

rustc 1.71.0-nightly (9d871b061 2023-05-21)
binary: rustc
commit-hash: 9d871b0617a4b3d6610b7cee0ab5310dcb542c62
commit-date: 2023-05-21
host: aarch64-apple-darwin
release: 1.71.0-nightly
LLVM version: 16.0.4

cc #56925