This is a wierd request, and potentially a bad thing to do.  But, that's your issue.  :-)

Your code isn't querying for the values of the Config_Object__c anywhere.   This is a custom object, and there can obviously be multiple records in that object, each with different stored queries and query criteria.  So, how are you going to determine which Config_Object__c record you want.  Again, your issue, I'll assume you want the most recently created one.

global class HF_Survey_OneMonth Implements Schedulable 
{
    
    global void execute(SchedulableContext sc)
    {
        sendSurvey();
    }
    
    
    public void SendSurvey()
    {
        // Get the most recently created config object.
        Config_Object__c config = [select HFSurveyCode__c, Survey_Date__c, SOQL_Query__c from Config_Object__c order by CreatedDate Desc limit 1];

        List<Opportunity> oppList = Database.query(config.SOQL_Query__c);                     
                    
             List<Account> accList = new List<Account>();
             
                   for(Opportunity opp:oppList)
                     {
                        if(opp.AccountId!= null)
                        {
                          Account acc = opp.Account;

// Why are you doing this IF statement?  You do the same things for both cases.
                          if(acc.Survey_Code__c != String.valueOf(config.HFSurveyCode__c))   // refer to the config object queried above.
                           {
                             string oppcode= opp.Id;
                             acc.Survey_Code__c = String.valueOf(config.HFSurveyCode__c);  // Isn't this redundant?
                             acc.Survey_Dt__c = config.Survey_Date__c;
                             acc.Survey_Opp_Id__c = oppcode.subString(0,15);  // Don't do the substring.  SF takes care of correctly handling Id's
                           }                  
                        
                       else if(acc.Survey_Opp_Id__c != opp.Id)
                          {
                             string oppcode= opp.Id;
                             acc.Survey_Code__c = String.valueOf(config.HFSurveyCode__c);
                             acc.Survey_Dt__c = config.Survey_Date__c;
                             acc.Survey_Opp_Id__c = oppcode.subString(0,15);
                          }
                         accList.add(acc); 
                        }
                     }
                update accList;          
              
     }
  }

However:

1. You should add a bunch of Try/Catch around several things here because the potential for bad queries is vast.

2. What happens to your code if the query stored in the Config object is, literally:   "Select Peanuts from classic comix from the 1950s".  Or, even better, "#T9834ugrewn3(*9r2", or even null.  So, if you're going to let users store queries, you've better be sure they are valid queries.  I'd think it's better to store the values that you want the user to be able to change and then build the query string yourself.  At least then you can use validation rules to check the values, and you'll always have the fields that you require.

Best, Steve.