You are using a normal JavaScript solution to this problem, but React uses a virtual DOM and expects DOM elements to be re-rendered when state changes. Therefore, I recommend leveraging React state to update the XY position of elements in the virtual DOM, but still using CSS.

Working DemoHere Or the code can be found here:

import { useState, useRef, useLayoutEffect } from "react";
import "./styles.css";

type BoxXYPosition = { x: number; y: number };

export default function App() {
  const startBox = useRef(null);
  const startBoxPosition = useRef({ x: 0, y: 0 });

  const endBox = useRef(null);

  const [boxPosition, setBoxPosition] = useState({
    x: 0,
    y: 0
  });
  const { x, y } = boxPosition;
  const hasMoved = Boolean(x || y);

  const updatePosition = () => {
    if (!endBox.current) return;

    const { x: endX, y: endY } = endBox.current.getBoundingClientRect();
    const { x: startX, y: startY } = startBoxPosition.current;

    // "LAST" - calculate end position
    const moveXPosition = endX - startX;
    const moveYPosition = endY - startY;

    // "INVERT" - recalculate position based upon current x,y coords
    setBoxPosition((prevState) => ({
      x: prevState.x !== moveXPosition ? moveXPosition : 0,
      y: prevState.y !== moveYPosition ? moveYPosition : 0
    }));
  };

  useLayoutEffect(() => {
    // "FIRST" - save starting position
    if (startBox.current) {
      const { x, y } = startBox.current.getBoundingClientRect();
      startBoxPosition.current = { x, y };
    }
  }, []);

  // "PLAY" - switch between start and end animation via the x,y state and a style property
  return (
    

      
Transition Between Points
      

        

          {hasMoved ? "End" : "Start"}
        
        

          

        
      
      
        Move to {hasMoved ? "Start" : "End"}
      
    
  );
}

During sleep, the browser may have time to recalculate the CSSOM box (also known as "execution reflow"). Without it, your transform rules won't actually apply.
In fact, the browser will wait until it's really needed to apply your changes and update the entire page box model, because doing so can be very expensive.
When you do something like

element.style.color = "red";
element.style.color = "yellow";
element.style.color = "green";

All CSSOMs will see is the latest status, "green". The other two were discarded.

So in your code, when you don't let the event loop actually loop, you will never see the transStr value either.

However, relying on 0ms setTimeout is a problem call, there is nothing to ensure that the style is recalculated at that time. Instead, it's better to force a recalculation manually. Some DOM methods/properties do this synchronously. But keep in mind that reflow can be a very expensive operation, so be sure to use it occasionally, and if there are multiple places in your code that require this operation, be sure to connect them all so that a single reflow can be performed. p>

const el = document.querySelector(".elem");
const move = () => {
  el.style.transition = "";
  const transStr = `translate(150px, 0px)`;
  el.style.transform = transStr;
  const forceReflow = document.querySelector("input").checked;
  if (forceReflow) {
    el.offsetWidth;
  }
  el.style.transition = "transform .5s";
  el.style.transform = "";
}
document.querySelector("button").onclick = move;

.elem {
  width: 100px;
  height: 100px;
  border: 1px solid grey;
}
.parent {
  display: flex;
  padding: 3rem;
}

force reflow
move