TreeSelect does not include its value in form formData

Describe the bug

The TreeSelect component's selected value is not being included in the form's formData when the form is submitted. This prevents its value from being retrieved with formData.get('name'), making it unusable for standard form submissions.

Reproducer

https://stackblitz.com/edit/vitejs-vite-b2hhqpew?file=src%2FApp.tsx

1. Select an item from the TreeSelect component.
2. Click the "Submit" button.

System Information

Environment

primereact: 10.9.7
react: 19.1.1

Expected Behavior

When the form is submitted, the TreeSelect component should contribute its value to the form's formData object. The formData.get('name') method should return the value of the selected node.

Start with the StackBlitz reproducer's src/App.tsx and run the form submission after selecting a TreeSelect item. Trace the TreeSelect form submission path to determine why formData.get('name') lacks the selected value. Done means the selected node value is included in the form's formData and can be retrieved with formData.get('name').