[ux] Export flow does not show result status

**Issue**
After exporting a data set in the Label Studio web interface, the export settings pop-over panel remains shown and no success or failure status notification is displayed.
This makes it unclear to user what happened and if their export action was successful, the only way to check if the export was successful is to inspect their file system for exported files. This ux issue is especially relevant when exporting large datasets and users not paying attention to the process (but they should be able to inspect success or failure when returning to their desk after fetching a latte ;) ).

**To Reproduce**
Steps to reproduce the behavior:
1. Go to the project overview
2. Click on a project
3. Click on 'Export' to open the export pop-up panel
4. Select an export output format (any will do)
5. Scroll down to find the 'Export' button
6. Click 'Export'
7. Observe, that after exporting, no success or failure notification message is shown, and that the export pop-over panel is still being displayed

**Expected behavior**
After selecting an export output format and clicking 'Export', I would expect the export pop-over panel to disappear, and a notification message being displayed outlining the result of the export action: either a successful export or a failure (preferably with an error message / code).

**Screenshots / screenrecording**

**Environment:**
- OS: macOS Tahoe 26.2
- Browser: Firefox 146.0.1
- Label Studio version 1.22.0