How to run python script in background on a permanent job on a VPS?

Use supervisor. It automatically restarts the process according to the criteria.

A minimal Conf:
[program:worker]
command=python /root/test.py
stdout_logfile=/var/log/worker.log
autostart=true
autorestart=true
user=root
stopsignal=KILL
numprocs=1

If you use relative paths in the system, be sure to use the directory parameter.
By default the script is run from /

systemd

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