@InvocableMethod annotation should be used to call Apex from Einstein BOT.

Sample Apex Class:

public class EinsteinChatBotController {  
 
    public class CaseOutput { 
     
        @InvocableVariable( required=true ) 
        public String sStatus; 
    } 
     
    public class CaseInput { 
     
        @InvocableVariable( required=true ) 
        public String sCaseNumber; 
         
    } 
 
    @InvocableMethod(label='Get Case Status') 
    public static List < CaseOutput > fetchCaseStatus( List < CaseInput > listCaseInputs ) { 
     
        List < CaseOutput > objOutputs = new List < CaseOutput >(); 
        CaseOutput objOutput = new CaseOutput(); 
        Set < String > strCaseNumbers = new Set < String >(); 
        for ( CaseInput objCaseInput : listCaseInputs ) 
            strCaseNumbers.add( objCaseInput.sCaseNumber ); 
        objOutput.sStatus = [ SELECT Status FROM Case WHERE CaseNumber IN: strCaseNumbers LIMIT 1].Status; 
        objOutputs.add( objOutput );  
        return objOutputs; 
     
    } 
 
}  

Apex Class action setup in Einstein Bot:

Permission Set sfdc.chatbot.service.permset:
Make sure the Apex Class is added to the Permission Set sfdc.chatbot.service.permset.