issue cleared.
The problem was introduced NOT on Tuleap side.

The reason Tuleap start failed from after-upgrade script came from upgrades of Server Control Panel "custom scripts" module.
To be more precise, the way multi-line scripts are interpreted changed.

nope,
there is a defect in after upgrade script indeed:
http://tuleap-documentation.readthedocs.io/en/latest/installation-guide/update.html

This works:

service tuleap stop
service nginx stop
yum update

The following sequence DOES NOT start tuleap (at least now, when Tuleap is up to date and there is nothing to do)

/usr/lib/forgeupgrade/bin/forgeupgrade --config=/etc/tuleap/forgeupgrade/config.ini update
/usr/share/tuleap/tools/utils/php56/run.php --module=nginx
service nginx start
service tuleap start

Thoughts:
I can not check if the after-upgrade script will start Tuleap in case there was a REAL upgrade (I guess I'll have to wait till next week for new upgrades to appear). For now, I just run "service Tuleap start" manually.

Hello,

What's the result of this command on the server:
service tuleap status