Freeze on "Saving Project data ..."

### Apache NetBeans version

Apache NetBeans 27

### What happened

Sometimes, after having modified a project from the dedicated screen and saved it, a small dialog appears with the words "Saving project data ..." which cannot be closed and the operation never ends.

### Language / Project Type / NetBeans Component

Java with Ant > Java Web Application

### How to reproduce

Open project properties, change a value (for example the binary format) and save

### Did this work correctly in an earlier version?

Apache NetBeans 26

### Operating System

debian 12

### JDK

openjdk 17

### Apache NetBeans packaging

Apache NetBeans binary zip

### Anything else

_No response_

### Are you willing to submit a pull request?

No

No source file or test is named. First reproduce the freeze through the Java with Ant > Java Web Application project-properties flow, changing a value such as the binary format and saving; done means project data saves successfully and the dialog closes.

Written by the indexing model from the issue text.