Honest question - how are you planning to source candidates in the first place? stack-auth is a two person YC startup and you were previously at another YC startup. I would expect you to tap the YC network for candidate referrals that probably will need little to zero tech evaluation?

I would probably skip a take-home for candidates at all for now. You probably have some specific pain points already. Try to find experienced TypeScript developers with some experience similar to your pain points and recommended to you by people in your network.

If you made me create a take-home assignment, I might make it rather open-ended and say do a compare/contrast of the stack-auth REST API versus one of the other options out there using any programming language and be prepared to describe code in both examples and strengths/weaknesses? This will help you maybe identify developers who self-select on "I'm interested in the stack-auth problem space . . . " Plus, that feels like a reasonably-sized effort for a candidate to me and could maybe be fun.

If you had a technical component during actual interviews, I think it is totally ok to ask someone to code up a small, simple Typescript example function of limited scope. Frankly, that's probably enough for you to get "yes/no" hiring signal.

I'm, err, older than you and will gently ask that you don't focus entirely on people who graduated since you did.