Teams by default doesn't expose the mailbox attached to the 365 group. I would keep the Shared mailbox how you have it and just utilize Teams itself with SharePoint etc. Unless you plan on doing additional training on how to use the Office 365 group in Outlook, which in my opinion contradicts Teams.
Keep the Shared mailbox for whatever you need it for, and if you want it inside the Team, you can just set a forward on the Shared Mailbox and send it to a channel inside the new Team. Right click a channel and "Get e-mail address" and you can use that e-mail address as the forward address. This way you get all the e-mail into the channel as new conversations that can be discussed.
There is also new Outlook integration where you should be able to take e-mail into Teams as well from Outlook and then respond to that e-mail from Teams.
There's no way to convert a shared mailbox to Group or Team, and in general it's challenging to import messages into a group/team mailbox. Also, group mailboxes lack a lot of functionalities you might be currently using with the shared mailbox, even simple things as rules or being able to access folder other than Inbox are missing.
It you want to use the developer@ address for the Team mailbox, you will have to remove it from the shared mailbox first, then set it to the Team.