Here is how you could achieve what you want. Notice I added your object keys in quotes, because they contain -, it wouldn't work other way.

const colors = {
  "colors-1": [{ color: "blue" }],
  "colors-2": [{ color: "gray" }, { color: "red" }],
  "colors-3": [{ color: "white" }]
};

function findPropertyByValue(colors, value) {
  for (let color in colors) {
    if (colors[color].some((c) => c.color == value)) {
      return color;
    }
  }
  return ""; // if there isn't one
}
console.log(findPropertyByValue(colors, "red"));

Here is a solution using find and some.
It takes the entries of the colors object and finds the entry which has an element with the input color.
The find returns an entry with [key,value] so to get key take the 0th element

Here I assumed that a single color has a unique key.
added the ?. before [0] (optional chaining - access only if available) so that when a color that is not found is input there will be no errors (returns undefined). || operator used to return a message like "not found" if the find step returns undefined

const colors ={
'colors-1': [{color: 'blue'}], 
'colors-2': [{color: 'gray'}, {color: 'red'}], 
'colors-3': [{color: 'white'}]
}

const findPropertyByValue = (obj,col) => Object.entries(obj).find(([k,v])=>v.some(({color}) => color===col))?.[0] || 'not found'


console.log(findPropertyByValue(colors,'white'))
console.log(findPropertyByValue(colors,'gray'))
console.log(findPropertyByValue(colors,'red'))
console.log(findPropertyByValue(colors,'blue'))
console.log(findPropertyByValue(colors,'green'))

You can try this:

const colors = {
  "colors-1": [{ color: "blue" }],
  "colors-2": [{ color: "gray" }, { color: "red" }],
  "colors-3": [{ color: "white" }],
};

function findPropertyByValue(obj, colorName) {
  return Object.entries(obj).find((entry) =>
    entry[1].some((color) => color.color === colorName)
  )?.[0];
}

console.log(findPropertyByValue(colors, "red"));
console.log(findPropertyByValue(colors, "not in list"));

And this solution will return all fields with specified color:

const colors = {
  "colors-1": [{ color: "blue" }],
  "colors-2": [{ color: "gray" }, { color: "red" }],
  "colors-3": [{ color: "white" }],
  "colors-4": [{ color: "white" }, { color: "red" }],
};

function findPropertyByValue(obj, colorName) {
  return Object.entries(obj).reduce(
    (acc, entry) =>
      entry[1].some((color) => color.color === colorName)
        ? [...acc, entry[0]]
        : acc,
    []
  );
}

console.log(findPropertyByValue(colors, "red"));
console.log(findPropertyByValue(colors, "not in list"));