Use Object.keys() to generate an array of the object keys ([0,1,2,3]). Loop through that array and check the id at each.

const data = {
    0: {
        id: 1912,
        title: 'Books',
    },
    1: {
        id: 1958,
        title: 'Brands',
    },
    2: {
        id: 2037,
        title: 'Logo',
    },
    3: {
        id: 2038,
        title: 'Colour',
    },
};

const updatedData = { id: 1912, title: 'The Books' };

Object.keys(data).forEach((el) => {
    if (data[el].id === updatedData.id) {
        data[el] = updatedData;
    }
});

As for React, I'd suggest that you should mutate your object for the update.

You can use Object.entries to get keys (your indices) and values (your inner object which you want to update), and then use map to populate your updatedData on found data with updatedData.id

const data = {
    "0": {
        "id": 1912,
        "title": "Books",
    },
    "1": {
        "id": 1958,
        "title": "Brands",
    },
    "2": {
        "id": 2037,
        "title": "Logo",
    },
    "3": {
        "id": 2038,
        "title": "Colour",
    },
}

const updatedData = {id: 1912, title: 'The Books'}

const result = Object.entries(data).map(([key, value]) => value.id === updatedData.id ? { [key]: { ...value, ...updatedData } } : { [key]: value })

console.log(result)