No, assuming it’s a UL-certified smart plug, there’s no problem at all. Especially if it’s a quality, name-brand product.
If it’s a no-name Amazon thing with unknown internals, it could definitely cause problems. But in that case I’d be more worried about your home wiring than the Tidbyt: Cheap smart plugs could expose you to hackers, or even cause a fire - Which? News
The Hictkon Smart Plug with Dual USB Ports, available on Amazon Marketplace, has been poorly designed, with the live connection far too close to an energy-monitoring chip. This could cause an arc – a luminous electrical discharge between two electrodes – which poses a fire risk, particularly to older homes with older wiring.