1.5-room apartment - Kitchen renovation

If you want to replace the sink and the stove, then you will surely need a new countertop as well. Then you can also replace the handles and remove those old-fashioned trims on the cabinets and take down the granny curtain at the window ;-). It will look completely different right away.

At first, I thought while reading: ... then you might as well remove everything“ But you hit the nail on the head... single-bowl sink without a draining board and a stylish black countertop and handles that pick up the black. The tile backsplash can also be covered with that or another matching countertop. The wood "look" has to fit in somewhere. Then it can look quite nice.

Lay linoleum flooring in the desired color (dark wood structure?) over the existing covering.
Coat the countertop with epoxy in the desired design. (just search on YouTube how to do it)
The fronts in white are quite OK. Paint the wood-colored parts dark (roll on).
New handles in a matching dark color or metal?
Stick an aluminum-laminated covering in front of the tile backsplash; it is only 3 mm thick.
Silicone joint between countertop and wall covering. (looks better than those stupid profiles).

Whether a new sink is necessary? Properly polish it and a stainless steel sink looks like new. Right? They aren’t that expensive either.

But as already said, just make a deal with the tenant and don’t invest anything.

Does a regular tabletop appliance fit in place of the refrigerator under the worktop?

I have to measure again. I almost think that no normal refrigerator fits there. Of course, ideally I wouldn't put one in, but if only one fits... Unfortunately, the cabinets are not white. It's a kind of "cream-colored," which leans slightly towards yellow. Therefore, I don't know if a dark/black worktop would look good. In addition, the boards inside the cabinets have the same color as the worktop. In other words, the worktop, strips in front of the cabinets, and boards inside all have the same color. A dark worktop and light wooden boards inside? And the strips in front of the cabinets are certainly hard to get in the same color as the worktop.

I meant to remove the skirting boards under the cabinets without replacement. That is very outdated. People had that in the 90s. Cream-colored fronts still exist today, they are called Magnolia... ;) Replace the handles with metal ones and re-cover the back panel (maybe in the same color as the floor - what should go there?) and make the transition to the countertop with a silicone joint, as icandoit wrote. That looks much better. Then a new faucet and a thorough cleaning. It is amazing what that alone can do.

I meant the strips as well. You just have to live with the holes for the mounting in the cabinets. I would also prefer metal handles. But they might visually clash with the wood. By backing panel, you probably mean the tile backsplash? As I said, I would like to replace the countertop, but I have concerns about how it will look with the cream-colored (slightly yellowish) cabinets and the wooden beams in the cabinets.

The floor will be something made of linoleum or PVC that matches visually in color.