Initialize cache directory in isolation

Creating and initializing the cache directory is interruptible; this
avoids a pathological case where interrupting a cache write can cause
the cache directory to never be properly initialized with its supporting
files.

Unify `Cache.mkdir` with `Cache.set` while I'm here so the former also
properly initializes the cache directory.

Closes #12167.

testing/test_assertrewrite.py

@@ -1731,8 +1731,8 @@ class TestEarlyRewriteBailout:
                     import os
                     import tempfile
 
-                    with tempfile.TemporaryDirectory() as d:
-                        os.chdir(d)
+                    with tempfile.TemporaryDirectory() as newpath:
+                        os.chdir(newpath)
                 """,
                 "test_test.py": """\
                     def test():