Hi Timothy Smith,
You just need to add else after if inside the loop,
You can use this code directly it will help you.
 

trigger CaseHandlerCountAlert on Case (after insert) {
    
    //Case trigger that will send email alert when 8 cases are created within 7 days.
    String messageToSend;
    List <String> ListOfMessages = new List <String>();
    Set <Id> AcctIds = new Set <Id>();
    String messageBody;
    
    List < AggregateResult > AggregateResultList = [SELECT AccountId, Account.Name name, COUNT(Id) co
                                                    FROM Case
                                                    WHERE CreatedDate = LAST_N_DAYS:7 AND Id IN :Trigger.New
                                                    GROUP BY AccountId, Account.Name
                                                    HAVING COUNT(Id) >= 8
                                                   ];
    
    Map < Id, String > accountIdEmailmessageMap = new Map < Id, String > ();
    
    for (AggregateResult aggr: AggregateResultList) {
        String messageToSend = 'Account name: ' + aggr.get('name') +
            ' has ' + (Integer) aggr.get('co') +
            ' cases opened in the last 8 days.';
        Id accId = (Id) aggr.get('AccountId');
        accountIdEmailmessageMap.put(accId, messageToSend);
        AcctIds.add(accId);
    }
    
    
    List < Case > caseList = [SELECT Id, AccountId, Account.Name, Parent_Project_if_applicable__r.Implementation_status__c,
                              Parent_Project_if_applicable__r.PM_Implementation_Status__c,
                              Parent_Project_if_applicable__r.RCM_Implementation_Status__c,
                              Parent_Project_if_applicable__r.Resource_Coordinator_Email__c,
                              Parent_Project_if_applicable__r.Client_Advisor_Email__c                      
                              FROM Case
                              WHERE AccountId IN: AcctIds];
    
    List<Messaging.SingleEmailMessage> lstASingleEmailMessage = new List<Messaging.SingleEmailMessage>();
    List<Messaging.SingleEmailMessage> lstBSingleEmailMessage = new List<Messaging.SingleEmailMessage>();
    
    for (Case cl: caseList) {
        
        if (cl.Parent_Project_if_applicable__r.Implementation_status__c == 'Live - Closed Project' ||
            cl.Parent_Project_if_applicable__r.PM_Implementation_Status__c == 'Live - Closed Project' ||
            cl.Parent_Project_If_Applicable__r.RCM_Implementation_Status__c == 'Live - Closed Project') {
                
                String messageBody = accountIdEmailmessageMap.get(cl.AccountId);
                
                List<String> emailaddr = new List<String>();
                emailaddr.add('CustomerSuccessManagers@test.com');
                
                Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
                mail.setSenderDisplayName('Support');
                mail.setToAddresses(emailaddr);   
                mail.Subject = 'Multiple cases created alert message';
                mail.setPlainTextBody(messageBody);
                lstASingleEmailMessage.add(mail);
                
            }else{
                String messageBody = accountIdEmailmessageMap.get(cl.AccountId);        
                
                List<String> emailAdds = new List<String>();
                emailAdds.add(cl.Parent_Project_if_applicable__r.Resource_Coordinator_Email__c);
                emailAdds.add(cl.Parent_Project_if_applicable__r.Client_Advisor_Email__c);
                
                Messaging.SingleEmailMessage amail = new Messaging.SingleEmailMessage();
                amail.SetSenderDisplayName('Support');
                amail.setToAddresses(emailAdds);
                amail.Subject = 'Multiple cases created alert message';
                amail.setPlainTextBody(messageBody);
                lstBSingleEmailMessage.add(amail);
                
            }  
    }
    Messaging.SendEmailResult[] r = Messaging.sendEmail(lstASingleEmailMessage);
    Messaging.SendEmailResult[] r = Messaging.sendEmail(lstBSingleEmailMessage);
    
}

If you found it useful please appreciate my efforts and mark it as the best answer

Regards,
Soyab