Move content from the mkdocs.public.yml into the template (#11246)

Closes https://github.com/astral-sh/uv/issues/11242

docs/requirements-insiders.txt

@@ -1,7 +1,9 @@
 # This file was autogenerated by uv via the following command:
 #    uv pip compile docs/requirements-insiders.in -o docs/requirements-insiders.txt --universal -p 3.12
 babel==2.15.0
-    # via mkdocs-material
+    # via
+    #   mkdocs-git-revision-date-localized-plugin
+    #   mkdocs-material
 black==23.10.0
     # via -r docs/requirements.in
 certifi==2024.7.4
@@ -19,6 +21,10 @@ colorama==0.4.6
     #   mkdocs-material
 ghp-import==2.1.0
     # via mkdocs
+gitdb==4.0.12
+    # via gitpython
+gitpython==3.1.44
+    # via mkdocs-git-revision-date-localized-plugin
 idna==3.7
     # via requests
 jinja2==3.1.4
@@ -71,8 +77,11 @@ mergedeep==1.3.4
 mkdocs==1.5.0
     # via
     #   -r docs/requirements.in
+    #   mkdocs-git-revision-date-localized-plugin
     #   mkdocs-material
     #   mkdocs-redirects
+mkdocs-git-revision-date-localized-plugin==1.3.0
+    # via -r docs/requirements.in
 mkdocs-material @ git+ssh://git@github.com/astral-sh/mkdocs-material-insiders.git@38c0b8187325c3bab386b666daf3518ac036f2f4
     # via
     #   -r docs/requirements-insiders.in
@@ -105,6 +114,8 @@ pymdown-extensions==10.8.1
     # via mkdocs-material
 python-dateutil==2.9.0.post0
     # via ghp-import
+pytz==2025.1
+    # via mkdocs-git-revision-date-localized-plugin
 pyyaml==6.0.1
     # via
     #   mkdocs
@@ -118,6 +129,8 @@ requests==2.32.3
     # via mkdocs-material
 six==1.16.0
     # via python-dateutil
+smmap==5.0.2
+    # via gitdb
 uc-micro-py==1.0.3
     # via linkify-it-py
 urllib3==2.2.2