at least in England, if you use an e-scooter while under the influence of alcohol, that equates to a motoring offence whereby incurring (car) driving licence penalties, driving licence disquaifications (bans), fines, and imprisonment all apply, depending on circumstances and severity. I'm not sure if/why it would be different anywhere else
And any bike lane infrastructure would benefit e-scooters anyway, so riding them in the road at 30mph below the flow of traffic is a sad hill to die on.