feat: position properties panel opposite to sidebar (#7647)

## Problem

When sidebar is positioned on the right, the properties panel also
appears on the right, causing both panels to compete for space and
creating a poor layout.

## Solution

Properties panel now dynamically positions itself opposite to the
sidebar:
- Sidebar left → Properties panel right (default)
- Sidebar right → Properties panel left

## Changes

- Modified `LiteGraphCanvasSplitterOverlay.vue` to conditionally render
properties panel based on sidebar location
- Updated splitter refresh key to recalculate layout when sidebar
position changes
- Added dynamic close button icon in `RightSidePanel.vue` that points in
the correct direction

## Testing

- Created E2E tests to verify positioning behavior
- Manually verified visual behavior in browser

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-7647-feat-position-properties-panel-opposite-to-sidebar-2ce6d73d365081049683e74c8d03dbdd)
by [Unito](https://www.unito.io)

browser_tests/tests/propertiesPanel/propertiesPanelPosition.spec.ts

@@ -0,0 +1,86 @@
+import { expect } from '@playwright/test'
+
+import { comfyPageFixture as test } from '../../fixtures/ComfyPage'
+
+test.describe('Properties panel position', () => {
+  test.beforeEach(async ({ comfyPage }) => {
+    // Open a sidebar tab to ensure sidebar is visible
+    await comfyPage.menu.nodeLibraryTab.open()
+    await comfyPage.actionbar.propertiesButton.click()
+  })
+
+  test('positions on the right when sidebar is on the left', async ({
+    comfyPage
+  }) => {
+    await comfyPage.setSetting('Comfy.Sidebar.Location', 'left')
+    await comfyPage.nextFrame()
+
+    const propertiesPanel = comfyPage.page.getByTestId('properties-panel')
+    const sidebar = comfyPage.page.locator('.side-bar-panel').first()
+
+    await expect(propertiesPanel).toBeVisible()
+    await expect(sidebar).toBeVisible()
+
+    const propsBoundingBox = await propertiesPanel.boundingBox()
+    const sidebarBoundingBox = await sidebar.boundingBox()
+
+    expect(propsBoundingBox).not.toBeNull()
+    expect(sidebarBoundingBox).not.toBeNull()
+
+    // Properties panel should be to the right of the sidebar
+    expect(propsBoundingBox!.x).toBeGreaterThan(
+      sidebarBoundingBox!.x + sidebarBoundingBox!.width
+    )
+  })
+
+  test('positions on the left when sidebar is on the right', async ({
+    comfyPage
+  }) => {
+    await comfyPage.setSetting('Comfy.Sidebar.Location', 'right')
+    await comfyPage.nextFrame()
+
+    const propertiesPanel = comfyPage.page.getByTestId('properties-panel')
+    const sidebar = comfyPage.page.locator('.side-bar-panel').first()
+
+    await expect(propertiesPanel).toBeVisible()
+    await expect(sidebar).toBeVisible()
+
+    const propsBoundingBox = await propertiesPanel.boundingBox()
+    const sidebarBoundingBox = await sidebar.boundingBox()
+
+    expect(propsBoundingBox).not.toBeNull()
+    expect(sidebarBoundingBox).not.toBeNull()
+
+    // Properties panel should be to the left of the sidebar
+    expect(propsBoundingBox!.x + propsBoundingBox!.width).toBeLessThan(
+      sidebarBoundingBox!.x
+    )
+  })
+
+  test('close button icon updates based on sidebar location', async ({
+    comfyPage
+  }) => {
+    const propertiesPanel = comfyPage.page.getByTestId('properties-panel')
+
+    // When sidebar is on the left, panel is on the right
+    await comfyPage.setSetting('Comfy.Sidebar.Location', 'left')
+    await comfyPage.nextFrame()
+
+    await expect(propertiesPanel).toBeVisible()
+    const closeButtonLeft = propertiesPanel
+      .locator('button[aria-pressed]')
+      .locator('i')
+    await expect(closeButtonLeft).toBeVisible()
+    await expect(closeButtonLeft).toHaveClass(/lucide--panel-right/)
+
+    // When sidebar is on the right, panel is on the left
+    await comfyPage.setSetting('Comfy.Sidebar.Location', 'right')
+    await comfyPage.nextFrame()
+
+    const closeButtonRight = propertiesPanel
+      .locator('button[aria-pressed]')
+      .locator('i')
+    await expect(closeButtonRight).toBeVisible()
+    await expect(closeButtonRight).toHaveClass(/lucide--panel-left/)
+  })
+})