There is no guarantee here that this will only execute once.

1. Is that potentially concerning in your use case? Or is your use case "idempotent", meaning it's okay for it to happen multiple times, but would be preferred to happen only once?
2. If it is not concerning in your use case, we should consider that you are introducing a utility that others might consume in the future. You should add a code comment clarifying that effect should be idempotent, and the caller should be okay with it potentially be called more than once if effect is ever changed.

In this case the effect is about displaying invitation modal. So displaying it twice should be avoided but isn't a huge issue. I'm going to add comments that explain that it's possible for an effect to run multiple times.

I can also spend some time thinking about making this safer.

I modified the logic so that now it's extremely unlikely that an effect might run twice - the only serious case is when saving to async storage fails - then the next run of the app will result in running the effect again.

Yes, according to the docs https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/await, for non-thenable object

An already-fulfilled Promise is constructed and used.

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/await#conversion_to_promise