fix: Use correct lychee cache file location

lychee does not support --cache-dir option. Default cache location is .lycheecache.

Changes:
- Remove --cache-dir from lychee-action args
- Update actions/cache path from .github/.lychee.cache to .lycheecache
- Update .gitignore to ignore .lycheecache (not .github/.lychee.cache)

This resolves the --cache-dir option error and properly caches the cache file.

Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>

Author: KATO-Hiro

.github/workflows/link_checker.yml

@@ -13,11 +13,11 @@ jobs:
       - name: Restore lychee cache
         uses: actions/cache@0057852bfaa89a56745cba8c7296529d2fc39830 # v4.3.0
         with:
-          path: .github/.lychee.cache
+          path: .lycheecache
           key: cache-lychee-${{ github.ref }}
           restore-keys: cache-lychee-
 
       - uses: lycheeverse/lychee-action@8646ba30535128ac92d33dfc9133794bfdd9b411 # v2.8.0
         with:
-          args: --cache --cache-dir .github/.lychee.cache --max-cache-age 14d --quiet "docs/**/*.md" "monthly_changelog/**/*.md" "README.md" "CONTRIBUTING.md"
+          args: --cache --max-cache-age 14d --quiet "docs/**/*.md" "monthly_changelog/**/*.md" "README.md" "CONTRIBUTING.md"
           fail: true

.github/workflows/link_checker_for_modified_files.yml

@@ -24,12 +24,12 @@ jobs:
         if: steps.changed-files.outputs.any_changed == 'true'
         uses: actions/cache@0057852bfaa89a56745cba8c7296529d2fc39830 # v4.3.0
         with:
-          path: .github/.lychee.cache
+          path: .lycheecache
           key: cache-lychee-${{ github.ref }}
           restore-keys: cache-lychee-
 
       - uses: lycheeverse/lychee-action@8646ba30535128ac92d33dfc9133794bfdd9b411 # v2.8.0
         if: steps.changed-files.outputs.any_changed == 'true'
         with:
-          args: --cache --cache-dir .github/.lychee.cache --max-cache-age 14d --quiet ${{ steps.changed-files.outputs.all_changed_files }}
+          args: --cache --max-cache-age 14d --quiet ${{ steps.changed-files.outputs.all_changed_files }}
           fail: true

.gitignore

@@ -121,4 +121,4 @@ __pycache__/
 site/
 
 # Lychee cache
-.github/.lychee.cache
+.lycheecache