dev: include Markdown link checks in the local lint suite (#25287)

## Which issue does this PR close?

- Part of #21048. The issue stays open for the other checklist items.

## Rationale for this change

`dev/rust_lint.sh` is the local mirror of the CI lint jobs, but it does
not run the Markdown link check. CI runs
`ci/scripts/markdown_link_check.sh` in `dev.yml`. A developer can push a
broken internal link after a clean local lint run and then see the
failure only in CI. This PR adds the existing checker to the local
suite.

## What changes are included in this PR?

- `dev/rust_lint.sh` runs `ci/scripts/markdown_link_check.sh` as a
read-only step, after the workflow install check and before the Rust
documentation build. The `--write` and `--allow-dirty` flags never reach
it.
- The runner loads `LYCHEE_VERSION` from
`ci/scripts/utils/tool_versions.sh` and installs that version when
`lychee` is missing. An installed `lychee` is used as is, which is the
runner's existing policy for other tools.
- `ci/scripts/markdown_link_check.sh` becomes executable, because the
runner invokes each registered script directly. The script body,
`lychee.toml`, the file selection, and the GitHub workflow do not
change.
- `docs/source/contributor-guide/testing.md` documents the new behavior
and keeps the standalone instructions.

## What is the testing strategy for this PR?

- A disposable fixture with stubbed steps and tools: the checker runs
once with no arguments in check mode and in both write modes, a missing
`lychee` triggers exactly the pinned install command, a present `lychee`
triggers no install, and a checker failure stops the suite before the
later steps.
- A disposable clone with an injected broken internal link: the
standalone checker and `./dev/rust_lint.sh` both fail with the same exit
code and name the file. After the fix, the full suite passes.
- The real checker and the full `./dev/rust_lint.sh` pass on this branch
with `lychee` 0.23.0.

## Are there any user-facing changes?

No. Developers get the link check in the local lint suite. CI is
unchanged.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Author: kumarUjjawal

ci/scripts/markdown_link_check.sh

@@ -22,7 +22,9 @@
 #
 # Note: The installed checking tools (e.g., taplo) are not guaranteed to match
 # the CI versions for simplicity, there might be some minor differences. Check
-# `.github/workflows` for the CI versions.
+# `.github/workflows` for the CI versions. When this script installs a missing
+# tool that has a pinned version in `ci/scripts/utils/tool_versions.sh`, it
+# installs that pinned version. An already installed tool is used as is.
 #
 #
 #
@@ -84,10 +86,15 @@ while [[ $# -gt 0 ]]; do
 done
 
 SCRIPT_NAME="$(basename "${BASH_SOURCE[0]}")"
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+
+# Load the tool versions shared with CI (for example, LYCHEE_VERSION).
+source "${SCRIPT_DIR}/../ci/scripts/utils/tool_versions.sh"
 
 ensure_tool "taplo" "cargo install taplo-cli --locked"
 ensure_tool "hawkeye" "cargo install hawkeye --locked"
 ensure_tool "typos" "cargo install typos-cli --locked"
+ensure_tool "lychee" "cargo install lychee --locked --version ${LYCHEE_VERSION}"
 
 run_step() {
   local name="$1"
@@ -107,6 +114,7 @@ declare -a WRITE_STEPS=(
 
 declare -a READONLY_STEPS=(
   "ci/scripts/check_no_cargo_install_in_workflows.sh|false"
+  "ci/scripts/markdown_link_check.sh|false"
   "ci/scripts/rust_docs.sh|false"
 )
 

dev/rust_lint.sh

@@ -188,7 +188,12 @@ tested in the same way using the [doc_comment] crate. See the end of
 
 ## Documentation Link Checks
 
-Run the internal markdown link check locally:
+`./dev/rust_lint.sh` runs the internal markdown link check. If `lychee` is
+missing, the script installs the version pinned in
+`ci/scripts/utils/tool_versions.sh`. It uses an existing installation as is,
+even if the version differs from the pin.
+
+To run the check on its own:
 
 ```shell
 source ci/scripts/utils/tool_versions.sh
@@ -200,6 +205,7 @@ Notes:
 
 - The script is run with `bash` and is compatible with the default Bash on macOS (no `mapfile` dependency).
 - The CI configuration currently checks internal markdown links only. External `http(s)` and `mailto` links are excluded to avoid flaky failures.
+- The check only reports broken links. `./dev/rust_lint.sh --write` does not change them.
 
 When a link is broken, lychee prints the file and URL/path that failed. For example: