As a workaround please do the following on all mailbox servers
zmlocalconfig -e zimbra_use_owasp_html_sanitizer=FALSE
zmmailboxdctl restart
It did help me. Unfortunately it means that their new owasp sanitizing framework is disabled (https://wiki.zimbra.com/wiki/Zimbra_Releases/8.8.12/P3). But it fixes both attachments and printing problems, i. e. it fixes both cases : "Case 00850083 Upgrade from 8.8.12_P2 to 8.8.12_P3 breaks printing inline images"
"Case 00849909 Infinite attachement since 8.8.12P3 in mail window"
It also fixed some broken html messages in web client.
BTW:
Unfortunately the Zimbra support was not helpful at all in this case.
They made me execute 9 or 10 tests, as they thought we have been hacked seeing those 3 issues.
Only one test (grep ua=python-requests /opt/zimbra/log/access_log*) was positive (not really - only 404 responses), but the support told me: You have been hacked, reinstall your server.
Searching for this user-agent string on a internet facing webserver is the weakest indication possible...