Look for suitable cabinets for our utility room

The finished laundry can be folded directly into the laundry basket.

Under the washing machine and dryer, there is a pull-out drawer where the laundry basket is placed directly in front of and slightly below the appliances.

Take a look at "Waschbecken CLARO GRANDE auf Waschmaschine" Maybe something like that could be a solution ;-)

This is how it should look with the washing machine and dryer.

Next to it, a cheap kitchenette and sink

Knoxhult is already very cheap (for a kitchen) and could become interesting

You can get it even cheaper from Poco. If I were you, I would consider installing a modular unit after all. Then the work is much more fun when you have a nice work surface and matching (cheap) cabinets :)

For the cabinets where the washing machine and dryer stand, I would opt for good quality. Always remember what the cabinets have to withstand during the spin cycle. Nobilia cabinets are at least delivered assembled, which saves you the assembly compared to Ikea. And Ikea is not cheap either. I would simply compare.

The finished laundry can be folded directly into the laundry basket.

But you do need a surface on which to fold the laundry before putting it in the laundry basket.