I believe you only have to pay to put your app on the App Store. I’ve made apps for my iPhone before and never had to pay.
There's some tools to automate "refreshing" the app, but that requires you have some other computer that pushes a new app every week.
The "1 week" restriction is usually fine when you're developing (as you typically are continually rebuilding and updating when actively working on an app) but is clearly intended to avoid being a way to sideload apps without the developer account "nearby".
[1]: https://docs.sidestore.io/docs/faq/#why-is-my-account-gettin...