Do you know about the problem with the beeping or ticking sound in HomePod, first gen.? Is there any solution to this bug/problem?

There is one solution that may make this stop.

Unplug HomePod for over 24 hrs.

Plug HomePod back in

You can immediately proceed with the next set of instructions:

1. Unplug HomePod - wait 10 seconds, then plug HomePod back in.
2. Wait 10 seconds, then touch and hold your finger to the top of HomePod.
3. The white spinning light will turn red. Keep your finger down. 
4. Siri will say that your HomePod is about to reset. When you hear three beeps, you can lift your finger.

After you reset HomePod, you can set up HomePod again.

Reset HomePod or HomePod mini - Apple Support