Write full Jupyter notebook to stdout (#7748)

## Summary

When writing back notebooks via `stdout`, we need to write back the
entire JSON content, not _just_ the fixed source code. Otherwise,
writing the output _back_ to the file will yield an invalid notebook.

Closes https://github.com/astral-sh/ruff/issues/7747

## Test Plan

`cargo test`

crates/ruff_notebook/src/notebook.rs

@@ -414,11 +414,13 @@ impl Notebook {
     }
 
     /// Write the notebook back to the given [`Write`] implementor.
-    pub fn write(&self, writer: &mut dyn Write) -> anyhow::Result<()> {
+    pub fn write(&self, writer: &mut dyn Write) -> Result<(), NotebookError> {
         // https://github.com/psf/black/blob/69ca0a4c7a365c5f5eea519a90980bab72cab764/src/black/__init__.py#LL1041
         let formatter = serde_json::ser::PrettyFormatter::with_indent(b" ");
         let mut serializer = serde_json::Serializer::with_formatter(writer, formatter);
-        SortAlphabetically(&self.raw).serialize(&mut serializer)?;
+        SortAlphabetically(&self.raw)
+            .serialize(&mut serializer)
+            .map_err(NotebookError::Json)?;
         if self.trailing_newline {
             writeln!(serializer.into_inner())?;
         }