possibility of transferring the system in a USB Hard Disk

[DRONE7]

Huh.

I've been flashing uSD cards and USB thumbdrives from moOde/DietPi/Volumio/RPiOS/you-name-it disk images with Belena Etcher in Win10 and Linux Mint for several years with nary a problem. Worked first time, every time.

Regards,
Kent

You, me, and millions the world over...

https://www.balena.io/etcher/

Well it seems that flashing is the easy part. Then it seems that pi needs also some kind of firmware update to boot from a usb (in my case an ssd with a sata-usb cable. Is it so? In any case when I put it directly even to my latest pi4 8gb nothing happens.

Yes the Pi4 needs a firmware update to boot from USB.  That is explained on the Raspberry Pi Foundation site.
https://www.raspberrypi.org/documentatio...torageboot

and more here..
https://www.maketecheasier.com/boot-rasp...-from-usb/

Though I think it may still be beta so if you're not linux competent you might want to wait for the official RPI upgrade...?
Unless you know exactly what you're doing then you risk bricking your Pi.

USB to SATA/ssd drive should work provided the drive is adequately powered.
This is recommended to be from an external power supply and not the Pi.

Note that it has been reported that not all ssd drives will work as boot devices....not a MoOde or RPI thing but hardware manufacturers configurations.

https://www.jeffgeerling.com/blog/2020/i...-4-usb-ssd