There are different types ics. You absolute can stay as a type of programmer who concentrate on your own project with 0 people leadership. But you do need tech leadership. You are taking this kind of project because your are technically sufficient and that's your leadership.

It doesn't mean it's a solo project. It just means you have the technical direction and you can let ppl manager to handle ppl side of things and you do almost 100% tech side of work. If you have 0 tech leadership and can only work on tasks assigned to you, you are not even ic4 worthy, that's absolutely ic3 ie ng level.

Again this is more of a feature in big tech where this kind of projects are available

For that kind of person even IC1 is not a good fit instead I usually recommend they will do better as a QA Engineer, Support Engineer etc. in FAANG or software engineer at a non-tech company (gov contractor, healthcare etc.). At least at FAANG companies IC is not just coding, it’s mentoring, providing technical leadership, writing design docs, oncall, etc. This is not leadership in the sense of a people manager it’s being able to provide constructive feedback to other teammates and positively influence your team’s codebase, architecture and product. Basically being able to lead technical decisions and technical strategy.

SDE2 is a terminal level at Amazon FYI

Can SDEIIIs have/hire supportive staff to deal with the managerial tasks the don't like?

I once basically had a part time secretary and it was fantastic. A few hours a week could even be enough, it just frees up so much mental space. It boggles my mind this is not the norm.