Update Projects docs for new org+project switcher

docs/inspector/projects.mdx

@@ -16,8 +16,10 @@ Each project saves its own set of MCP servers. Switch between projects with one
 
 ## Getting Started
 
-1. **Click the project name** in the header bar
-2. **Create a project** - Click "Add Project" and give it a name
+The combined org and project switcher sits at the top of the sidebar. It shows your active project name and, below it, the organization it belongs to.
+
+1. **Click the switcher** at the top of the sidebar to open the context menu
+2. **Create a project** - Click the **+** icon next to the **Projects** heading and give it a name
 3. **Add your servers** - Configure your MCP servers in the Servers tab
 4. **Share with your team** - Click the share button and invite collaborators
 
@@ -33,6 +35,18 @@ When you switch projects, all servers disconnect automatically to give you a cle
   allowFullScreen
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+## Switching Organizations
+
+The **Organization** section at the top of the context menu shows your active organization. Click the organization chip to open a popover listing all your organizations and select a different one. Switching organizations reloads the sidebar with that organization's projects — no page reload required.
+
+- On desktop, hovering over the chip also opens the organization list.
+- The gear icon next to an organization name (visible to admins and owners) navigates to that organization's settings.
+- Per-project settings gears and member avatars are shown on each project row in the list.
+
+<Info>
+After completing an OAuth flow, you are returned to the organization you were in when the flow started, so you never land on the wrong organization after authenticating.
+</Info>
+
 ## Sharing Projects
 
 Project sharing lets your entire team work with the same servers. Set up your project once, invite your team by email, and everyone gets access to the same servers with the same configurations instantly.