There is no fixed limit for MMS attachment size. Internally it is an email message, and can handle pretty much anything any other email message can. (My carrier limited at 600KB last I looked).
It may be that the phone is set for a larger message than the carrier will accept: it may be that it takes that long for the carrier to reject the message. It may even be deliberate: because of a spam problem, the carrier may have decided to delay responding to messages it’s going to reject.
The size limit is based on the carrier. Android allows users to set the MMS attachment limit to whatever their carrier’s limit is, but otherwise it wouldn’t know unless you tell it.
MMS requires mobile data or wifi. Perhaps you reached your data limit?
“Unlimited Texts” likely only applies to SMS. A file attachment is sent via MMS and uses your data plan.
You may want to try sending a test message with a smaller attachment. Have you sent a file attachment before? If not, try sending a small 50-100kb file attachment and see if it even works. You might not even be set up for it; may need to edit the APN, etc.