Creating problem with cache plugins

Hi,

I have a website where the plugin is installed with W3 Total cache plugin and it looks like the site doesn’t save the preference for dark or light mode. Instead of that it shows the cached version to the users. I have recoded a video. Please check and let me know if there is any solution for this:

https://www.loom.com/share/c52485c3edda4e1f8e1dd990916eebc0

Thank you

The page I need help with: [log in to see the link]