bash – Piping nc to sed and evaluate datetime for each row

Could someone provide any idea, how could i pipe data from nc to sed (or awk, or anything) and evaluate and write to file a timestamp after each row?
What i have:

# cat /etc/systemd/system/ncserver.service
(Unit)
Description=netcat listener
After=network.target

(Service)
Restart=always
RestartSec=1
ExecStart=/usr/bin/bash -c '/usr/bin/nc -n -v -l -k -p 1313 >> /opt/data/$(hostname)-$(date -u +%%y%%m%%d-%%H).txt'

(Install)
WantedBy=multi-user.target

simple listener – receives text via raw tcp, sends into the file (restarts by cron once a day to generate new file)

I want to append current timestamp to each row of text coming (at the beginning or the end of the row, doesnt matter).
Tried sed, awk, but the problem is that i cannot evaluate date for each row – it evaluates only once, when service started.
Looks like this

109582 ?        Ss     0:00 /usr/bin/bash -c /usr/bin/nc -n -v -l -k -p 1313 | /usr/bin/sed 's/^/'$(date +%s)
 109583 ?        S      0:00 /usr/bin/nc -n -v -l -k -p 1313
 109584 ?        S      0:00 /usr/bin/sed s/^/1617555467;/g

Pipe may be not the answer at all, but i’m kinda limited by bash.
Any ideas?..