Hi Pierre,
Which version dish do you have? The original circular one (which is what I suspect), the rectangular RV/residential one, or the more square-ish High Performance/Maritime version?
In the US, the RV/Residential and HP/Maritime versions require either the Starlink router, or the Starlink power supply in the case of the HP/Maritime version.
The older circular dishes came with a router, but the router-to-dish cabling was standard ethernet, and you could send PoE down it to power it. I have one of those dishes in use, but they aren’t as performant as the newer ones, and aren’t sold or shipped as often here in the US anymore.