The synchronized modifier guarantees method body consistency

### Apache NetBeans version

Apache NetBeans 23

### What happened

When the "methodToBeInlined()" method is selected for the Inline method refactoring, it causes a refactoring bug, because the inline method contains a syx modifier, but after refactoring, there is no method body missing the syx modifier, resulting in a change in access permissions.

class SourceClass{
private boolean flag = false;
public synchronized void method() {
flag = true;
}
public void callerMethod(){
method() ;
}
}
​

### Language / Project Type / NetBeans Component

_No response_

### How to reproduce

When the "methodToBeInlined()" method is selected for the Inline method refactoring, it causes a refactoring bug, because the inline method contains a syx modifier, but after refactoring, there is no method body missing the syx modifier, resulting in a change in access permissions.

class SourceClass{
private boolean flag = false;
public synchronized void method() {
flag = true;
}
public void callerMethod(){
method() ;
}
}
​

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

Apache NetBeans 23

### Operating System

Windows11

### JDK

20

### Apache NetBeans packaging

Apache NetBeans provided installer

### Anything else

_No response_

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

No

Start with the Inline method refactoring entry point and reproduce the issue using the SourceClass example in the report. Trace how the synchronized modifier is handled when method() is inlined into callerMethod(); done means the refactoring preserves the method body's synchronization semantics and access behavior.

Written by the indexing model from the issue text.