I already have an account on the mobile phone but I would like to have an additional new one on the laptop, this is possible even if I use the same email address
You need an additional cell phone number, as far as I know, if nothing has changed since then.
WhatsApp only works on the mobile phone (unless you use an Android emulator)
You need a second cell phone number
So if FB has not made any changes with WA, then the WA "account" is still tied to a telephone number
So either set up a different mobile or landline number on the notebook and then you also need an Android simulator on it, as there's only one web interface, which however requires a mobile phone on which WA runs in parallel
You need a second number, otherwise there's no way. You can get a SIM card for as little as 5 euro at Edeka, Lidl and co.
There's WhatsApp web.