[Language Service] Fix project path on notebooks when running on Windows

source/pip/qsharp/_qsharp.py

@@ -40,6 +40,7 @@
 import os
 import sys
 import types
+from pathlib import Path
 from time import monotonic
 from dataclasses import make_dataclass
 
@@ -160,8 +161,7 @@ def __init__(
             # For now, we only support local project roots, so use a file schema in the URI.
             # In the future, we may support other schemes, such as github, if/when
             # we have VS Code Web + Jupyter support.
-            normalized_root = os.path.normpath(os.path.join(os.getcwd(), project_root))
-            self._config["projectRoot"] = "file://" + normalized_root
+            self._config["projectRoot"] = Path(os.getcwd(), project_root).as_uri()
 
     def __repr__(self) -> str:
         return "Q# initialized with configuration: " + str(self._config)

source/vscode/src/language-service/notebook.ts

@@ -147,7 +147,16 @@ function getQSharpConfigMetadata(notebook: vscode.NotebookDocument): object {
   if (data) {
     const dataString = new TextDecoder().decode(data);
     log.trace("found Q# config metadata: " + dataString);
-    return JSON.parse(dataString);
+    const dataStringJSON = JSON.parse(dataString);
+    // Re-normalize projectRoot URI if present.
+    // Python and VS Code have different URI normalization logic,
+    // so we need to parse and re-serialize it here.
+    if (typeof dataStringJSON.projectRoot === "string") {
+      const projectRootUri = vscode.Uri.parse(dataStringJSON.projectRoot, true);
+      dataStringJSON.projectRoot = projectRootUri.toString();
+    }
+
+    return dataStringJSON;
   } else {
     // Default to Unrestricted profile for notebooks when no explicit configuration is provided
     // This aligns with the Python qsharp runtime behavior