Thanks for your post @Andrew9 and welcome to our Community Forums.
To backup your emails you'll need to setup your emails onto an email client then archive or download them through the client's settings. There's instructions Here on how to set your emails up on a client.
Once you've done that we can then transfer your domain to your new provider, we'll just need their IPSTAG.
If you can send me a private message with this, we'll raise a support ticket on your account you can reply to with confirmation you're happy to go ahead then we'll raise a task with our NetOps team to carry out the transfer.
Let me know if you've got any further queries or need more help.
From 31st October 2022, I no longer have a regular presence here as I’ve moved on to a new role.