Is there an iPhone or Android app?
Not in a store: SOS works in your phone's browser, and you can add it to your home screen so it opens like an app.
What exists today
SOS is a website that works on phones, tablets and computers. It has no App Store or Google Play app today.
You can add SOS to your home screen. It then opens in its own window, without the browser bars.
A store app
Some Settings screens mention a store launch. There is no store app today, and those screens give no date.
What a browser cannot do
A few features are made for a phone app. These include reminders that appear on your phone and Face ID or fingerprint sign-in. They are not available in the browser.
In the browser, your Encrypted Vault is protected by a PIN.
What happens next
For now, adding SOS to your home screen is the way to open it like an app.