How can delete a draft for a no-reply sender?
After playing around with the app, I've found that this is something that Google messenger has overlooked. They don't have any option of clearing drafts.

After some research I found that it's safe to clear data of your messenger app. This will clear all drafts and unsent messages, but nothing else.
To do that, go to settings -> apps -> messages -> storage -> clear data.

Sent and received messages are not stored in the messaging app, rather they are stored in /storage/emulated/0/Android/data/com.android.providers.telephony.
(You might need a rooted phone to access this)
Therefore clearing the app data is not going to delete your messages.

I have tried this myself before recommending such a drastic move. (I did make a backup before that, just in case.)