Sorry there is no way to help with this with only that info.Waht are you showing the tile for ? It does in no way go with the peel and stck couter for sure. Is this a rental ? Right now with what you show a good white color for walls. to match the white of the "counter"

I can change the counter color - what would you suggest?

who owns the apt. ... "gross" should be addressed with new counters. that can be a health and safety matter and why do you want covering over...? new counters even butcher block or simple formica if budget is a concern.

Warm whites look good with the woodwork you show, but if there is any white in the room such as the countertop you have to make sure they are the same or complementary. So if you're going to change the countertop you need to decide on that before choosing a paint color. While it seems like a good idea to paint before you move in it is really helpful to at least be able to look at samples in the rooms you're painting at different times of the day to make sure you're choosing the right color.

Peel and stick counters last about a week before they too get gross and sticky.

It's a rental. Leave all the wood the oak color. Here's an article about whites that go with oak. Paint the entire apartment the same white. Use color via art, rugs, and furnishings to bring light and color into your small rooms. Put a great food poster on that door

https://julieblanner.com/kitchen-makeover-without-paint

This is from Society6.com, which has incredibly affordable prints of all subjects and colors for your new place. Choose some you like to add color and interest to your new place so you have something wonderful to look at in every room.

--Get new lighting for the kitchen with proper bulb wattage for the space.

--Do a deep cleaning of wood cabinets inside and out. Ditto the floors.

--Change out hardware on wood cabinets. Don't paint them.

--Forget about the slapping stick-on "wallpaper" on kitchen countertops. Ugh, just no. How much countertop do you need to cover? If only a little, spend a little $$$ on new laminate countertops. Or investigate Rustoleum to cover the current ones, but only after you read reviews, watch multiple YouTube videos on how to do it and what to expect.

You really need to give Houzz photos of the space from all four sides. So, do your deep cleaning of cabinets, floors, trim, walls. Paint everything a light, warm white as suggested above. Then take photos to get additional advice on how to deal with counters. A patterned laminate in warm white, light white to link with white tile, and light speckled or streaked pattern in light brown would make the cabinets look better and wouldn't cost a lot. And a BIG NO!!!! to that busy backsplash. Get white subway tile, some of which is seen in a corner of your photo:

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More info would help get you appropriate recommendations. Please explain if you are renting or buying the apartment. Renters usually need permission to paint.

Do you need the countertop cover-up because you need a short term solution before someone, maybe you, replaces the countertop?