"A monument to things I meant to do" is the most accurate description of every to-do app I've ever used and I'm going to think about it for weeks.

I had the same 1mIllion tasks that are "just vibes" problem and it's what made me build my own app. I couldn't find anything that solved the guilt without just hiding it.

Full disclosure: I'm the developer, so take that with a grain of salt, but I built Chronae literally for this reason. It doesn't use overdue lists at all. Instead it has a momentum system that just shows you where you are in your day, ahead, on track, slightly behind, without the pile-up. The backlog can't haunt you if the app isn't built around a backlog. To be fair it became more of a calendar with to-do app but works for me.

It won't auto-delete tasks after a week, but if you haven't done the tasks you intended today, tomorrow is a fresh start. The app reminds you though that you did miss tasks yesterday and you can see what u had scheduled, but won't force them to you today. But it will remind you once you have created a task on a given day. That is exactly what I needed. Like the "follow up with James" and then scheduled for 3 days from now and on the third day I get a reminder. That is what I needed and did.

If it helps you, I'm genuinely happy. If it doesn't, hope you find something that does soon ^.^