chore(ci): wire MATHLIB_CACHE_BASE_URL from a repository variable

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Author: marcelolynch

.github/workflows/build_template.yml

@@ -48,6 +48,10 @@ env:
   # are valid by-products of the Mathlib build. Build artifacts fetched from Lake's cache do
   # not necessarily satisfy this property.
   LAKE_NO_CACHE: true
+  # Read-base override for the cache tool: normally unset, so reads go to
+  # Azure. An operator sets the repository variable to move cache read
+  # traffic to another host, and clears it to move the traffic back.
+  MATHLIB_CACHE_BASE_URL: ${{ vars.MATHLIB_CACHE_BASE_URL }}
 
 jobs:
   build:

.github/workflows/lake_cache_shadow.yml

@@ -104,6 +104,9 @@ env:
   SHADOW_SCOPE: mathlib4-master-shadow
   # NOTE: STAGE_TARGETS is set per-job (not here) from the `targets` input, so
   # it can be overridden per dispatch — see the `build_and_stage`/`consume` env.
+  # Read-base override for the mathlib cache tool (the warm-start `cache get`);
+  # Lake's own cache ignores it. Normally unset, so reads go to Azure.
+  MATHLIB_CACHE_BASE_URL: ${{ vars.MATHLIB_CACHE_BASE_URL }}
 
 jobs:
   build_and_stage:

.github/workflows/olean_report.yaml

@@ -20,6 +20,12 @@ concurrency:
 permissions:
   contents: read
 
+env:
+  # Read-base override for the cache tool: normally unset, so reads go to
+  # Azure. An operator sets the repository variable to move cache read
+  # traffic to another host, and clears it to move the traffic back.
+  MATHLIB_CACHE_BASE_URL: ${{ vars.MATHLIB_CACHE_BASE_URL }}
+
 jobs:
   report:
     name: Prepare olean report

.github/workflows/remove_deprecated_decls.yml

@@ -21,6 +21,12 @@ on:
         default: false
         type: boolean
 
+env:
+  # Read-base override for the cache tool: normally unset, so reads go to
+  # Azure. An operator sets the repository variable to move cache read
+  # traffic to another host, and clears it to move the traffic back.
+  MATHLIB_CACHE_BASE_URL: ${{ vars.MATHLIB_CACHE_BASE_URL }}
+
 jobs:
   build:
     name: Remove outdated deprecated declarations