How do I create a group entity from floor area

All my lights are categorized to areas and floors.

How/Can I create a light group entity from all the lights that are defined on a certain floor?

You can’t because a Light Group doesn’t support templates. You need a template to produce a list of all light entities on a given floor.

There’s a way to use an automation, triggered at startup or similar system event, that would add all light entities on a given floor to an ‘old-style’ Group. That’s possible because old-style Groups have a group.set service call (which can be templated). However, the result will be a group entity, not a light entity (so it only supports on/off).