JSFiddle - React, Tailwind, and code Playground

JavaScript

var arr = [
    {
        Id: 1, Categories: [
            { Id: 1 },
            { Id: 2 }, 
        ]

    },
    {
        Id: 2, Categories: [
            { Id: 100 },
            { Id: 200 },
        ]

    }
];

var matches = [];
var needle = 101;

arr.forEach(function(e) {
    matches = matches.concat(e.Categories.filter(function(c) {
        return (c.Id === needle);
    }));
});

console.log(matches[0] || "Not found");