It does sound like snoring. That’s exactly what’s couple of mine sound like when snoring.
When you say you’re hearing it when they’re not asleep, what are they doing? You may or may not know this, but rabbits can nap with their eyes open. Do it can be deceiving whether they are sleeping or not!

Clover used to snore all the time when she was content, or when she was sound asleep. It was charming as all get out. Dainty girl bunny snores.

I’d be sitting in my chair going, “WTH is that noise?”  Clover at my feet, snoring.

My new bunny Vilde makes little sounds. He can make a grunting noise when he’s not happy (not happy has happened twice, because he’s been to the vet twice for two different shots – we’re in Europe where buns need shots). He can make other sounds at home, esp at night. Vilde had his heart and lungs checked at both vet visits and was given the all clear for insurance purposes. When my bridge bunny Bam had a respiratory infection, my vet heard it at once when she listened to his lungs. She did x-rays to find out the extent of the infection, so to be really sure, you could have your bun’s lungs x-rayed.

Other signs of a respiratory issue is that the bun sits and lies with its chin held high. This is in an effort to open the airways to get more air in. Some buns will try to breathe through their mouth, which is not normal for a rabbit, they should only ever breathe through their nose.

Buns can vary quite a lot in their tendency to vocalize. Some grunt or oink when they are expecting a treat. Some growl when they’re angry. Un-neutered buns often honk or oink when they are feeling courtshippy.

The best way to find out would be lung x-rays (my bunny didn’t need sedation for that) and blood tests. Blood tests can show if there’s some ongoing infection in the body.