I've got an independent short film project where I'm the only sound person involved. I've had to do everything from pre-production to post. What would be appropriate for credit(s)? Is there a blanket-term for someone who performs multiple roles?
You are firmly entrenched in a gray area. The terms that come to my mind regarding film credit are Supervising Sound Editor (traditional) or Supervising Sound Designer (more contemporary), although I really like the simplicity of Sound or Sound Design.
To tag on to Tim's answer, indeed is not uncommon to have more than one credit, so you should feel free to award yourself as many titles as you see appropriate.
I'd ask for two credits
production sound recordist or mixer listed with the production crew
sound editor listed with post production
Its not unheard of to have 2 credits, maybe check on IMDb to see what other people have done... if other film film makers see the credits and are looking for someone for either role then it would work better for you than one term to cover both, which doesn't exist afaik
When I do multiple sound-related duties for a project, I usually just ask for one credit specific to what I am focus on. "Sound Editor" is usually what I ask for.
Maybe I'm the only one, but when I see multiple credits for one person, it gives me a negative feeling towards the project. Perhaps it's all the terrible movies I watch on "watch it now" that have one person as the writer, director, editor, and star! I don't think it's fair to categorize sound like this, because on a low budget project it makes sense to have someone who knows sound to do all of it. On short films, I prefer to be the production recordist or boom op when I'm going to do the post production. But I digress....
Before attaching yourself to a project credit see how it turns out first. Under no circumstances do you want a credit to something that has compromsied sound due to budget.
If it is decent you would be favourite going down as sound supervisor as that post covers start to finish.
But in reality be true to yourself, if the job didn't require much planning or delegation I would as the chap above said and stick with 'sound'.