The useful gift for someone who rents is something they can unplug and carry to the next place. A sofa that needs a drill is a gift for the landlord.
Match the person, not a theme. Cold on the couch, no open flames allowed, cooks in a tiny kitchen, or just got the keys: those are four different presents.
The person who is always cold
A heated throw (on Amazon) lives on the couch, which is where a lot of apartment living actually happens. The Bedsure one linked here is 50 by 60 inches, faux fur on one side and sherpa on the other, with a timer and an auto shut-off. The color on that listing is a grey tie-dye. Cream, taupe and solid grey are on the same page if you want it quieter. It folds into a suitcase when they move. The listing says not to sleep on top of it, so it stays a lap blanket, not a bed layer.
If they sleep cold rather than sit cold, a bed-sized heated blanket is the larger version of the same idea. That list is in the winter bedroom upgrades.
A rental that cannot have a real flame
Plenty of buildings ban candles, and a cat makes the rule for you even when the lease does not. A candle warmer lamp (on Amazon) melts a jar from above with a bulb, so there is no wick. The Marycele one has a wood base, a post you can raise for a large jar, a dimmer, and a timer for 2, 4 or 8 hours. Two bulbs come in the box. On a nightstand it is also just a small lamp, which a dark rental usually needs anyway.
The cook with one free burner
Boiling water should not take the only burner that is not already holding a pan. A 1.7 liter stainless kettle (on Amazon) does tea, cocoa and the water for gravy, then goes in the next kitchen without an argument. On this Cosori the spout, inner lid and filter are stainless, and it shuts itself off.
The larger gift, if they actually cook, is a 6 quart enameled Dutch oven (on Amazon). One pot braises, bakes and goes to the table with the lid on. The evergreen Lodge works on a normal apartment stove, including induction. It is heavy, about 15 pounds empty, which is the cast iron doing its job and also the reason not to store it on a high shelf. More on feeding people from a small kitchen is in the holiday hosting list.
Someone who just got the keys
Light is the first thing a rental gets wrong, and the floor is the second. A dimmable floor lamp (on Amazon) plugs in, needs no electrician, and leaves with them. A washable 5 by 7 rug (on Amazon) covers the flooring they did not choose and goes in the wash when winter shoes have had a month at it. Neither one puts a hole in the wall.
Skip the oversized furniture, the built-in shelving, and anything that only works if they own the ceiling. The present they will still have in two apartments is the one that unplugs.