Hi!

Is it possible to register an operator automatically when Blender starts?
I have tried to put the .py-file in
./config/blender/scripts/startup/
and
./config/blender/scripts/

but that doesn't seem to work (are there any requirements on the name of the file?).

Do I maybe have to create an addon containing the operator?

yes, you should make it an addon and enable it by default
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