Could alien civilizations be watching Earth right now?

Possibly in principle, yes — but there is no evidence that any alien civilization is currently watching Earth.

If an advanced civilization existed nearby, it could potentially notice Earth in a few ways:

• Radio leakage: Humans have been broadcasting high-power radio, television, and radar signals into space for about a century. Those signals travel at the speed of light, creating an expanding radio bubble roughly 100 light-years in radius, so only civilizations within that distance could have had time to receive the earliest ones.
• Atmospheric signs of life: An observer with very advanced telescopes could study Earth’s atmosphere, including when Earth transits the Sun, and look for gases such as oxygen, ozone, and methane, which can be clues that life exists.
• Technosignatures: In principle, very sensitive observations might detect industrial pollutants or other artificial features, though that would be much harder than noticing life-friendly chemistry.

The main limitation is distance and light travel time: any aliens observing us would be seeing Earth as it was in the past, not in real time.

So the short answer is: yes, it’s physically possible that some civilization could detect Earth, but we have no empirical evidence that anyone is doing so.