Why can only some emails be set to IsExternallyVissible = false?

According to this Know issue(https://trailblazer.salesforce.com/issues_view?id=a1p3A0000018BuDQAU), I cannot set the flag IsExternallyVisible to false via the EmailsMessage trigger. The workaround is a Future method that I created. This does not work for all emails. Some emails can be changed and others not. But there is no recognisable pattern. I wrote a test and it failed. But I do not understand why. This is my test:

@isTest
public class EmailMessageTest {
    @testSetup 
    static void setup() {
        TestDataFactory.prepareForTest();
    }    @isTest
    static void mailExternalyVisible() {
        List<Id> emailIds = new List<Id>();        
		Case c = new Case();
        c.Subject = 'Test';  
        c.Description = 'testing';
        c.Status ='New';
        c.Priority = 'Medium';
        c.Origin = 'Email';
        insert c;        //Insert emailmessage for case
        EmailMessage email = new EmailMessage();
        email.FromAddress = 'test@abc.org';
        email.Incoming = True;
        email.ToAddress= 'test@xyz.org';
        email.Subject = 'Test email';
        email.HtmlBody = 'Test email body';
        email.ParentId = c.Id; 
        insert email;        
		emailids.add(email.id);        
		Test.startTest();
        //call future methode
        EmailMessageTriggerHandler.changeVisibility(emailIds);
        Test.stopTest();        EmailMessage emailRec = [Select id, IsExternallyVisible from EmailMessage where parentId = :c.id limit 1];
        System.assertEquals(false,emailRec.IsExternallyVisible, 'Email should not be externally visible');    }
}

This is the future methode:

    @future
    public static void changeVisibility(List<ID> emailIds){
        System.debug('changeVisibility');
        List<EmailMessage> emailsToUpdate = [SELECT Id,Incoming,IsExternallyVisible,Status FROM EmailMessage WHERE Id IN :emailIds];
        System.debug('emailsToUpdate before');
        System.debug(emailsToUpdate);
        for(EmailMessage em : emailsToUpdate){
            System.debug('loop setting mail to false');
            em.IsExternallyVisible = false;
        }
        System.debug('emailsToUpdate after');
        System.debug(emailsToUpdate);
        update emailsToUpdate;        
        emailsToUpdate = [SELECT Id,Incoming,IsExternallyVisible,Status FROM EmailMessage WHERE Id IN :emailIds];
        System.debug('emailsToUpdate after update');
        System.debug(emailsToUpdate);
    }

When I check the debug message I see that it has been reseted to true again. See attached image.

My Trigger for EmailMessages looks like that:

trigger EmailMessageTrigger on EmailMessage (after insert,before insert) {    if(Trigger.isAfter && Trigger.isInsert){        
EmailMessageTriggerHandler.createCaseNotifications( Trigger.new );        
List<Id> emailIds = new List<Id>();        
for(EmailMessage email:Trigger.new){            
emailIds.add(email.Id);        
}        
if(!System.isFuture() && !System.isBatch()){            
EmailMessageTriggerHandler.changeVisibility(emailIds);        
}    
}

#Sales Cloud}