When "systemctl stop syslog-ng", what impact does it have on existing sessions? (4256321)

Yes when the command is issued,  it tries to close off all connections gracefully.

When the command "systemctl stop syslog-ng" is issued, syslog-ng is requested to stop, through the default stop action used by systemd.

In this case that means that a SIGTERM signal is sent to the syslog-ng process. Upon its reception, syslog-ng will try to flush all of its output buffers: if it has disk buffers defined, then the associated memory buffers will be saved in the disk buffer files, and if there is no disk buffer defined, then syslog-ng will try to send out all messages in the memory buffers and will terminate all incoming and outgoing network connections.