@GAuber If you are migrating from H2 to MySQL, then you should not do that through a service.
It's a one-off process, which should be done completely separately from trying to run as a service.
The log in Admin > Troubleshooting > Logs should be the same as you see in the file log, if you've setup SystemD to log to a file.
So first do that:
https://www.metabase.com/docs/latest/operations-guide/migrating-from-h2.html
Then when you are running on MySQL, then shutdown, configure your service environment variables to reference the MySQL and otherwise follow what is listed in the service guide:
https://www.metabase.com/docs/latest/operations-guide/running-metabase-on-debian.html
Do not set host or port, the defaults are fine, when using Nginx as a reverse-proxy.