Diagnosis
A dirty or moist top surface interferes with the capacitive touch sensors. Even a thin film of grease or lotion can cause issues.
How to Fix It
Power off and unplug the HomePod. Use a dry, soft, lint-free cloth to thoroughly clean the entire top glass surface. Make sure your fingers are completely dry before testing. The touch area is the entire illuminated center, not just the +/- signs.
If That Didn't Work
There's a software setting that disables touch. In the Home app, select the HomePod, tap the gear icon, and scroll to "Touch Accommodations." Ensure it's toggled OFF. If it's on, touch is disabled.
Heads Up
The touch controls are designed for brief, firm taps, not long presses or swipes (except for volume). A long press activates Siri. If you're wearing gloves or have a screen protector on your finger, it won't work.