Configuring Mailgun for warmup can be a little tricky considering it, like AWS SES, doesn't have an inbound IMAP.
We permit using SMTP from one provider and an IMAP from another. So you can use SMTP from Mailgun and IMAP from any other service you like.
Outgoing Mail (SMTP) Server
Server - smtp.mailgun.org (US) | smtp.eu.mailgun.org (EU)
Port - 465 or 587
User - Your email
Password - Your API Key
The likes of AWS SES, SendGrid, SendinBlue, Mailgun do not provide IMAP. So you will need the IMAP of another mail provider like Google, Zoho, AWS Workmail, etc.
A general rule is to use the IMAP of where you receive replies to your emails but we place no restrictions on this. You can use whatever IMAP you prefer.
Also note, you can create a filter to keep your inbox productive and auto-archive emails from Murlist.