[Inspector UXR] Layout explorer delay

_This issue has been broken out of https://github.com/flutter/devtools/issues/2890_

## Delay when changing values

There's a slight delay when clicking boxes/dropdowns in the Layout Explorer:


This makes the DevTools feel sluggish to use and affects the overall user experience and the quality of usage.

Start by reproducing the delay when clicking boxes and dropdowns in the Layout Explorer, using the linked GIF as the expected symptom. Trace the interaction from the Layout Explorer UI and identify what makes DevTools feel sluggish; done means those value changes respond without the reported delay.

Written by the indexing model from the issue text.