To set scene, I am a newbie to Jira and I do not have massive amounts of experience on Email servers. I would appreciate some help.
Set up incoming handlers but do not appear to be receiving new tasks into the project. As far as I can tell for this method I do not need to set up anything on our email servers.
Set up is as follows;
Name: Create a New Issue on Jira
Project: I have chosen a project to receive issues
Server: Default Cloud Server
Delay: Will not let me alter
Handler: Create a new issue or let me add to an issue
Project: Same project as above
Issue type: Story
Strip quotes: Blank
Catch email: Blank
Bulk: Accept the email for processing
Forward email: blank
Create users: Tick
CC Assignee: Tick
CC Watcher: Tick
It looks like you are trying to follow a guide such as Creating issues and comments from email for setting up a mail handler. However that guide is specifically for Jira Software and Jira Core.
Jira Service Desk has a different mechanism in order to create customer requests from email. It has to do this because in order for the Core/Software mail handler to work in a project to process those messages, the senders email addresses have to correspond to email addresses that Jira knows about as licensed Jira users on that site.
Service Desk mail handlers do not have this requirement. They are designed to be able to work with unlicensed Jira users (ie, users in the Service Desk Customer role). As such there is a different guide for setting this up in Service Desk specific projects that I would recommend, see Jira Service Desk Cloud: Receive requests from an email address. Following these steps instead will help to make sure that these emails are created into Service Desk requests, and not just Jira issues.
I hope this helps.