Sliding door with soundproofing: What options/providers are available?

Either you want soundproofing, then you need a door. Or you want a sliding door, then there is no good soundproofing. That's just how it is, unfortunately. Not airtight against smells anyway.

How often do you have to go to the wardrobe? Every minute? If not, is it perhaps reasonable to close the door to the kitchen the 2 or 3 times a day?

Thank you for your tips. We will now have to weigh whether it will be a sliding door or a regular door.