The problem is that it doesn't store "unit" meta-data for stderr, so you can not see stderr logs with journalctl -u nameOfUnit or systemctl status nameOfUnit
I do not find this to be the case. Right now I'm looking at the journal and observing the existence of _SYSTEMD_UNIT fields for messages that have been written to a process's standard error stream.
Yup. It is possible that your service is buffering output before actually writing it to the standard error stream. Try attaching to it with strace -e write PID and observe whether it is actually calling write(2, "some message"..., somenumberofbytes).
To approach this from the other direction, try this program:
import sys, time
while True:
print('test out', flush=True)
print('test error', file=sys.stderr, flush=True)
time.sleep(5)