Honest question here, why do you feel you have to write types to get anything done?
I usually use minimal types when prototyping (just turn off the noImplicitAny flag) and you get practically the same experience as if you were just using js.
From here you can use an incremental approach and write types if you want.
I realize this kind of defeats the point of having a typed language, but I don’t feel it requires you to write out all the types before you can get anything done.

Don't be ashamed of the stuff you build :) Takes a while to get there. Most people never release the stuff they make, and even then most don't get those kinds of downloads and reviews.
Awesome charango app btw

Just see it as them trying to do their job. It's their job to get a good candidate and make sure the company doesn't have to invest more in him/her than necessary.
Granted some recruiters are kind of blunt about it, but just keep in mind, you'll probably get a higher salary if you negotiate it and ask him to give you a figure, instead of you giving him one upfront.

I'd never thought of an employer as a service provider to outsource all the stuff and I'm not good at. Definitely makes sense if you see this that way.

Good luck! Hope you do great