That looks like wood, might be custom?

I know this is probably too late but if you are still looking there are often vintage live edge coffee tables on auction sites that could be upcycled as vanity counters.

I think you are trying to tone with what is there but in a small space I think you need to go as light as possible. I would be looking for a nearly white granite with warmer veining such as artic white (bear in mind they are often called different things by different suppliers) I also like stone type products like Silestone

I think you see bars (serving beers) with stools and no overhang. These are fine for a social setting where one person might be sitting with their back to the bar chatting to others in the room. If you intend to use the bar for food you need to face the island so will need the recommended leg room. Could you swap the 600 deep cabinets for 300mm deep? The cost of new carcasses might not be too bad. You should also talk to your kitchen fitter as he may be able to install them after the quartz.