[private-server] minor fixes

Author: capcom6

docs/getting-started/private-server.md

@@ -148,19 +148,25 @@ To run the server, you'll need:
     API URL: https://private.example.com/api/mobile/v1
     Private Token: your-secure-token-here
     ```
+    !!! note "API URL Path"
+         The API URL **must** include the `/api/mobile/v1` path. Using just the base URL (e.g., `https://private.example.com`) will not work.
 
 3. **Activate connection**  
     1. Switch to **Home** tab
     2. Activate **Cloud server** switch
-    3. Restart the app using the bottom button
+    3. **Tap the "Offline" button** to initiate the connection and registration process
+    4. Wait for the app to establish connection (button will change to "Online")
 
 !!! success "Successful Connection"
-    New credentials will appear in **Cloud Server** section when configured properly:
+     After successful connection, credentials will be **automatically generated** and appear in the **Cloud Server** section:
     ```text
     Username: A1B2C3
     Password:  z9y8x7...
     ```
 
+!!! info "Automatic Registration"
+    No manual registration step is required. Username and password are generated automatically on the first successful connection to the server.
+
 ### Password Management 🔑
 
 Identical to [Cloud Server mode](public-cloud-server.md#password-management).

docs/getting-started/public-cloud-server.md

@@ -125,13 +125,15 @@ Change the notification channel in the app settings:
    Launch app → Toggle "Cloud Server"
 
 2. **Go Online**  
-   Tap the "Offline" button → Becomes "Online"
-   
+   Tap the "Offline" button to initiate connection and registration process → Button will change to "Online" when connected
+    
 3. **Get Credentials**  
-   They will be generated by the server.
+    Credentials will be **automatically generated** and appear in the **Cloud Server** section after successful connection:
    <center>
       <img src="/assets/cloud-server.png" alt="Cloud Server credentials screenshot"/>
    </center>
+    !!! info "Automatic Registration"
+        No manual registration step is required. Username and password are generated automatically on the first successful connection to the server.