JSFiddle - React, Tailwind, and code Playground

HTML

<pre id="out"></pre>

JavaScript

let users = [
  {
    name: 'user 1',
    services: [
      {
        title: 'service 1',
        categories: ['category 1', 'category 2']
      },
      {
        title: 'service 2',
        categories: ['category 3', 'category 4']
      },
      {
        title: 'service 3',
        categories: ['category 5', 'category 6']
      }
    ]
  },
  {
    name: 'user 2',
    services: [
      {
        title: 'service 4',
        categories: ['category 7', 'category 8']
      },
      {
        title: 'service 5',
        categories: ['category 9', 'category 10']
      },
      {
        title: 'service 6',
        categories: ['category 11', 'category 12']
      }
    ]
  }
];

let filterBy = ['category 5', 'category 6']; // отфильтровать на наличие данных категорий в объекте.

const filtered = users.filter(user => filterBy.every(cat => user.services.some(service => service.categories.includes(cat))))

out.textContent = JSON.stringify(filtered, null, 4)