Make cache-write failures non-fatal (#12302)

## Summary

Closes https://github.com/astral-sh/ruff/issues/12284.

crates/ruff/src/cache.rs

@@ -180,12 +180,24 @@ impl Cache {
             .write_all(&serialized)
             .context("Failed to write serialized cache to temporary file.")?;
 
-        temp_file.persist(&self.path).with_context(|| {
+        if let Err(err) = temp_file.persist(&self.path) {
+            // On Windows, writing to the cache file can fail if the file is still open (e.g., if
+            // the user is running Ruff from multiple processes over the same directory).
+            if cfg!(windows) && err.error.kind() == io::ErrorKind::PermissionDenied {
+                warn_user!(
+                    "Failed to write cache file '{}': {}",
+                    self.path.display(),
+                    err.error
+                );
+            } else {
+                return Err(err).with_context(|| {
                     format!(
                         "Failed to rename temporary cache file to {}",
                         self.path.display()
                     )
-        })?;
+                });
+            }
+        }
 
         Ok(())
     }

crates/ruff/src/commands/format.rs

@@ -176,6 +176,7 @@ pub(crate) fn format(
         duration
     );
 
+    // Store the caches.
     caches.persist()?;
 
     // Report on any errors.