How can I check Caps Lock status without using so much CPU?

That loop launches cat through command substitution 50 times a second. The sleep keeps it from being a completely tight loop, but repeatedly starting processes is still unnecessary work.

If polling is good enough, try reading the brightness file with Bash's built-in read instead of cat, and increase the interval to something like 0.2 seconds. Check that the LED path exists and is readable before entering the loop. You may need to choose the right path if there is more than one matching LED.

I'd look at an event-driven option first. A Hyprland key binding could trigger a script when Caps Lock is pressed, rather than checking a file continuously.

The tricky bit is knowing the resulting state, not just noticing a keypress. Make sure the script reads the state after it changes, and test whether your binding still lets Caps Lock work normally.

Another route is to listen to keyboard input events. Linux input devices can report LED events, so a program could wait for a Caps Lock LED update and play the matching sound without a polling loop.

That is more involved than a shell loop. You need access to the appropriate input device and need to handle devices appearing or disappearing. Parsing the raw event structures directly also depends on their layout, so a proper input-event library is safer than assuming a fixed byte size.

One caveat: keyboard LED brightness isn't necessarily the same thing as the logical Caps Lock state. The LED can be controlled independently, and multiple keyboards can leave you reading the wrong device.

Decide whether you want the sound to follow a particular keyboard's indicator or the state used for typing. That choice affects which source you should monitor, and what should happen when no suitable keyboard is available.