I've tried searching this forum and also searching online but I can't seem to find a way of putting the key fob to sleep. Maybe that's not an option with Skoda.

What do I mean? On my Subaru, there is the facility to switch the key off, so its presence near the car door handle will not open the car keylessly. Instead the 'open' button has to be pressed to 'wake the key up'. This sleep mode is achieved by holding the 'open' button on the fob while simultaneously pressing the lock button twice in quick succession. So the key stops emitting a signal. I follow this procedure whenever I arrive home and hang the keys up in the key store near the front door. Obviously, it's an extra security feature.

Can I do something similar with the Karoq?

All I have ever seen, is that the fob will go to sleep, if not moving after a few minutes. Not much use, if wandering around, with key fob in pocket, but should be safe at home, in drawer or whatever.

The Subaru system is much better, as fitted to my much missed XV.

1 hour ago, Ooopnorth said:

Can I do something similar with the Karoq?

Yes.

Lock car with key-fob and within 2 seconds touch sensor on outside of door handle. This turns off Kessy (keyless entry) and you need to press the button on the key-fob to open door. Mine is set to only open drivers door unless two presses.

However this does not save you from car-jackers with an a booster aerial so after locking car always put key-fob in an RFID pouch. Mine key-fob lives in one except when I am driving.

I believe on newer models the key actually goes into a sleep mode after a few minutes of not being moved around. On older ones, the RFID pouch is a solution to this.