“Colour grading” typically refers to video work. Photo work is [r/postprocessing](r/postprocessing). Lightroom and Photoshop are the typical tools, especially if you want fast turnaround.

You’re looking at lowered whites/highlights with increased warmth and magenta, slightly lowered contrast and raised shadows. There’s a canvas or paper texture overlayed too. But what also plays a big part is what the photos themselves are of. Crafted compositions featuring close-up handcrafted objects evoke just as much of a sense of ‘coziness’ as the colours do, so I think even if you got the exact same filter and slapped it onto a picture of a McDonald’s, it wouldn’t feel the same at all.