I'm sorry he's so anxious.
You may believe that nothing out of the ordinary has happened lately - but to him, there may have been something that upset him that would not even register on an adult's radar. You'd be surprised how kids can get anxious over things that they are trying to process mentally that we parents never know about.
Is he still having no problems at all when you leave him at school? At day care or other people's houses? Is he clingy or reluctant for you to leave him at all when he wasn't before? It sounds like the answer is no, and if so -- that's good. You need to find out what it is about home that makes him anxious when other places or your leaving him in other places do not have this effect.
So think through his day and his environment:
Is it possible that he saw even part of a scary movie or TV show, or played or just saw some of a scary video game, at another kid's house if not at your house? Our daughter was able to hear the TV in her room since our house is very small, so when she was little we had to take care to use closed captioning so she couldn't hear TV after she was in bed.
Does he watch any TV or play video games or games on a smartphone (even innocent little games, not scary ones) at any time in the hours before bedtime? Pediatric studies have shown that kids who watch any screens of any type within two hours or so of bedtime have their sleep disturbed -- even if the content is "kid-friendly." The flickering screen is very stimulating, again, even if it's slow, kiddie content. If he's doing screen time anywhere near bed, he may be stimulated and sleeping badly leading to nightmares.
Is there a chance that something in his room that was once OK is now scaring him? Night lights can cast weird shadows that we adults don't notice but that kids see and fear. A moved chair, a blanket thrown over the back of something can cast disturbing shadows. Sit in his room with him after lights out and have him look hard at things with you.
Is it possible that he has heard something on the news, or from kids at school, about real-life cases where people disappear from their own homes? I can see that a kid would be jumpy about mom taking out the trash if he's heard from classmates about how a parent went out the door and never came back. Kids do try to scare each other with stories, real and imagined.
Has he possibly read, or been read, any books that depict kids on their own without any parents around? A LOT of kids' books these days are set in worlds where no parents are evident or taking part in the action, and many a classic kids' book and Disney movie pictures characters whose parents are not present or who are dead.
Pick over those kinds of things and then talk to him. He may still say "I don't know" when you talk to him -- if so, let it go, don't try too hard to drag a specific reason out of him, and for a while, just tell him when you're going to the basement or taking out the trash.
Even better, have him come down with you to help with the laundry, or have him take one trash bag alongside you so you take it out together -- that will distract him and engage him, and get his mind off whether you'll vanish. Just announce and reassure and don't overtalk it for now.
If it persists for months or gets worse, it would then be time to see the school counselor with him first, and go from there. But it sounds as if maybe he got a scare somehow, and is processing it. Just do what he wants for now and let him know where you'll be -- that is not coddling him, that's just reassuring him, and will make him more confident.