Facebook confirmed that they've rolled out a fix for this issue.
Monitoring · UTC
We're seeing that Buttons and Images are rendering correctly now in Messenger Web App.
Facebook's representatives also reported that the issue has been mitigated.
We'll keep monitoring the situation for some time before closing this incident.
Identified · UTC
You may notice Buttons and Images not getting displayed in Messenger Web App at the moment.
We have reported this issue to Facebook - more information to follow soon.