The problem is there in the approach of updating queryObject state . Since queryObject state is an object and if we try to directly modify the object like this :-

    setQueryObject((prevQueryObject) => {
      prevQueryObject.genders.push(name);
      return prevQueryObject;
    });
  

React does not recognise any change in the state since the object has the same reference so it doesn't update DOM. Therefore we need to create a deep copy of that object and set it back to the object state again so that change in object state is recognised and React updates the DOM.

    setQueryObject((prevQueryObject) => {
      return{...prevQueryObject,genders:[...prevQueryObject.genders,name]};
    
    });
 

Full Working Code here - CodeSandbox Link

Thanks to Yury i re-wrote the code and it works

import { useState } from "react";

function SideBar() {
  const [queryObject, setQueryObject] = useState({
    genders: [],
    availabilities: []
  });
  function handleChange(event) {
    const { name, checked } = event.target;

    if (name === "male" || name === "female") {
      if (checked) {
        setQueryObject((prevQueryObject) => {
          return {
            ...prevQueryObject,
            genders: prevQueryObject.genders.concat(name)
          };
        });
      } else {
        setQueryObject((prevQueryObject) => {
          return {
            ...prevQueryObject, 
            genders: prevQueryObject.genders.filter((e) => e !== name)
          }
        });
      }
      return;
    }

    if (name === "available" || name === "not available") {
      if (checked) {
        setQueryObject((prevQueryObject) => {
          return {
            ...prevQueryObject,
            availabilities: prevQueryObject.availabilities.concat(name)
          };
        });
      } else {
        setQueryObject((prevQueryObject) => {
          return {
            ...prevQueryObject,
            availabilities: prevQueryObject.availabilities.filter(
              (e) => e !== name
            )
          };
        });
      }
      return;
    }
  }

  return (
    <div>
      <input
        type="checkbox"
        checked={queryObject.genders.includes("male")}
        onChange={handleChange}
        name="male"
      />
      <span>Male</span>
      <input
        type="checkbox"
        checked={queryObject.genders.includes("female")}
        onChange={handleChange}
        name="female"
      />
      <span>Female</span>
      <br />
      <input
        type="checkbox"
        checked={queryObject.availabilities.includes("available")}
        onChange={handleChange}
        name="available"
      />
      <span>Available</span>
      <input
        type="checkbox"
        checked={queryObject.availabilities.includes("not available")}
        onChange={handleChange}
        name="not available"
      />
      <span>Not available</span>
    </div>
  );
}

export default SideBar;