Hi @SergioCostas,
I tried this but it did not fully end the snap-store process, so I was not able to update it.
Before that I had tried a system reboot but to no avail it would seem.
I had to end the process (either through kill <snap-store processId> or using the system monitor app), and I was then able to run sudo snap refresh snap-store.
As @jaime-cruz states, a more user-friendly way of updating the snap-store would be very welcome.