My first thought was RUBBISH - but I like to check these things out
First I checked the Liverpool system - no mention of only roads - but also no mention of them being allowed in cycle lanes or shared paths
which I would assume they would say if they were allowed
Also checked the manufacturers site - also no mention of the above
Then checked another area's regulation - still no mention
and also no mention of them being able to be used in any place that bikes (and legal ebikes) can go
which I found rather strange
Then I found this
Quote
Where you can use a trial e-scooter
You may use a trial e-scooter on the road (except motorways) and
in cycle lanes.
You must not use an e-scooter on the pavement.
Traffic signs with the following cycle symbol apply to e-scooters (unless a sign is displayed prohibiting e-scooters from that particular cycle way):
End Quote
from here
https://www.gov.uk/guidance/e-scooter-trials-guidance-for-users#where-you-can-use-a-trial-e-scooter
But if the regulation set in place by the city (etc) then I'm not sure what the rules would be