JSFiddle - React, Tailwind, and code Playground

JavaScript

const data = [
  {
    billed: "No",
    designation: "ASE",
    involvement: "Full Time",
    name: "Rishi Ranabhat",
    project: "ABC"
  },
  {
    billed: "No",
    designation: "ASE",
    involvement: "Full Time",
    name: "Biplap Bhattarai",
    project: "DEF"
  },
  {
    billed: "No",
    designation: "SE",
    involvement: "Part Time",
    name: "Ram k",
    project: "DEF"
  }
];

designations = [];
projects = [];
for (record of data) {

  // Count designations
	if (! designations[record.designation]) {
  	designations[record.designation] = 0;
  }
  designations[record.designation] = designations[record.designation] + 1;
  
  // Count projects
  if (! projects[record.project]) {
  	projects[record.project] = 0;
  }
  projects[record.project] = projects[record.project] + 1;
  
}

// Merge sets
const final = [designations, projects];

console.log(final);