feat: add dual-mode tree editor with Code Mode, variables, and markdown sync

Implements the full dual-mode tree editor (Plan Phases 1-5):

Backend:
- JSONB↔Markdown bidirectional serializer/parser with mistune
- Markdown validator with line/column error reporting
- 3 API endpoints: export-markdown, import-markdown, validate-markdown
- Variable extraction/resolution service ([USER_INPUT], [VAR], [SAVE_AS])
- Session variables JSONB column (migration 028)
- 39 tree markdown tests + variable service tests (403 total passing)

Frontend:
- Monaco-based Code Mode with custom Monarch tokenizer and dark theme
- Autocomplete for @node_id refs, type values, variable names
- Debounced validation (800ms) with inline Monaco error markers
- Syntax help panel (absolute overlay, toggleable)
- Starter template for new trees with valid cross-references
- Bidirectional metadata sync (name/description/category/tags frontmatter)
- Synchronous tree→markdown serializer (fixes async race condition)
- Pre-save validation blocks save on broken refs or missing tree name
- Mode-aware undo/redo: Monaco native in Code Mode, throttled zundo in Flow Mode
- Variable prompt modal and frontend resolver for session navigation

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/app/services/tree_markdown_validator.py

@@ -0,0 +1,93 @@
+"""
+Validation for ResolutionFlow tree markdown.
+
+Validates markdown without saving, returning detailed errors with line numbers.
+"""
+from app.services.tree_markdown_parser import parse_markdown_to_tree, ParseError
+
+
+def validate_tree_markdown(markdown: str) -> list[ParseError]:
+    """Validate tree markdown and return all errors/warnings.
+
+    This wraps the parser and adds additional semantic checks.
+
+    Args:
+        markdown: The markdown string to validate.
+
+    Returns:
+        List of ParseError objects with line, column, message, severity.
+    """
+    result = parse_markdown_to_tree(markdown)
+    errors = list(result.errors)
+
+    # If parsing completely failed, return early
+    if result.tree_structure is None:
+        return errors
+
+    # Additional semantic validation on the parsed tree
+    _validate_tree_semantics(result.tree_structure, errors)
+
+    return errors
+
+
+def _validate_tree_semantics(tree: dict, errors: list[ParseError]) -> None:
+    """Run semantic checks on a parsed tree structure."""
+    all_ids: set[str] = set()
+    has_solution = False
+
+    def _collect_ids(node: dict) -> None:
+        nonlocal has_solution
+        all_ids.add(node.get("id", ""))
+        if node.get("type") == "solution":
+            has_solution = True
+        for child in node.get("children", []):
+            _collect_ids(child)
+
+    _collect_ids(tree)
+
+    if not has_solution:
+        errors.append(ParseError(
+            line=1, column=1,
+            message="Tree must have at least one solution node",
+            severity="warning"
+        ))
+
+    # Check for empty required fields
+    def _validate_node(node: dict) -> None:
+        ntype = node.get("type", "")
+        nid = node.get("id", "")
+
+        if ntype == "decision":
+            if not node.get("question", "").strip():
+                errors.append(ParseError(
+                    line=1, column=1,
+                    message=f"Decision node '{nid}' has an empty question",
+                    severity="warning"
+                ))
+            if not node.get("options"):
+                errors.append(ParseError(
+                    line=1, column=1,
+                    message=f"Decision node '{nid}' has no options",
+                    severity="warning"
+                ))
+
+        elif ntype == "action":
+            if not node.get("title", "").strip():
+                errors.append(ParseError(
+                    line=1, column=1,
+                    message=f"Action node '{nid}' has an empty title",
+                    severity="warning"
+                ))
+
+        elif ntype == "solution":
+            if not node.get("title", "").strip():
+                errors.append(ParseError(
+                    line=1, column=1,
+                    message=f"Solution node '{nid}' has an empty title",
+                    severity="warning"
+                ))
+
+        for child in node.get("children", []):
+            _validate_node(child)
+
+    _validate_node(tree)