Update checkbox property name and add doc examples (microsoft#183920)

Fixes microsoft#183829

Author: alexr00

src/vs/workbench/api/common/extHostTreeViews.ts

@@ -93,7 +93,7 @@ export class ExtHostTreeViews implements ExtHostTreeViewsShape {
 		const hasHandleDrag = !!options.dragAndDropController?.handleDrag;
 		const hasHandleDrop = !!options.dragAndDropController?.handleDrop;
 		const treeView = this.createExtHostTreeView(viewId, options, extension);
-		const proxyOptions = { showCollapseAll: !!options.showCollapseAll, canSelectMany: !!options.canSelectMany, dropMimeTypes, dragMimeTypes, hasHandleDrag, hasHandleDrop, manuallyManageCheckboxes: !!options.manuallyManageCheckboxSelection };
+		const proxyOptions = { showCollapseAll: !!options.showCollapseAll, canSelectMany: !!options.canSelectMany, dropMimeTypes, dragMimeTypes, hasHandleDrag, hasHandleDrop, manuallyManageCheckboxes: !!options.manageCheckboxStateManually };
 		const registerPromise = this._proxy.$registerTreeViewDataProvider(viewId, proxyOptions);
 		return {
 			get onDidCollapseElement() { return treeView.onDidCollapseElement; },

src/vscode-dts/vscode.proposed.treeItemCheckbox.d.ts

@@ -52,7 +52,38 @@ declare module 'vscode' {
 		 * By default, when the children of a tree item have already been fetched, child checkboxes are automatically managed based on the checked state of the parent tree item.
 		 * If the tree item is collapsed by default (meaning that the children haven't yet been fetched) then child checkboxes will not be updated.
 		 * To override this behavior and manage child and parent checkbox state in the extension, set this to `true`.
+		 *
+		 * Examples where {@link TreeViewOptions.manageCheckboxStateManually} is false, the default behavior:
+		 *
+		 * 1. A tree item is checked, then its children are fetched. The children will be checked. TODO @alexr00 there's a bug here
+		 *
+		 * 2. A tree item's parent is checked. The tree item and all of it's siblings will be checked.
+		 *   - [ ] Parent
+		 *     - [ ] Child 1
+		 *     - [ ] Child 2
+		 *   When the user checks Parent, the tree will look like this:
+		 *   - [x] Parent
+		 *     - [x] Child 1
+		 *     - [x] Child 2
+		 *
+		 * 3. A tree item and all of it's siblings are checked. The parent will be checked.
+		 *   - [ ] Parent
+		 *     - [ ] Child 1
+		 *     - [ ] Child 2
+		 *   When the user checks Child 1 and Child 2, the tree will look like this:
+		 *   - [x] Parent
+		 *     - [x] Child 1
+		 *     - [x] Child 2
+		 *
+		 * 4. A tree item is unchecked. The parent will be unchecked. TODO @alexr00 there's a bug here
+		 *   - [x] Parent
+		 *     - [x] Child 1
+		 *     - [x] Child 2
+		 *   When the user unchecks Child 1, the tree will look like this:
+		 *   - [ ] Parent
+		 *     - [ ] Child 1
+		 *     - [x] Child 2
 		 */
-		manuallyManageCheckboxSelection?: boolean;
+		manageCheckboxStateManually?: boolean;
 	}
 }