Answer
Do you have to submit a PWA to an app store?
No. A PWA installs directly from the browser with no app store involved at all — that is one of its core advantages. Submitting to the Google Play Store, Microsoft Store or Apple App Store is entirely optional and is done purely for extra discoverability, using wrappers like a Trusted Web Activity (Android) or PWABuilder-generated packages (Windows, and a WKWebView-based wrapper for iOS).
Default distribution
A user visits your URL, the browser evaluates installability criteria, and they install straight from there — no review, no store account needed.
Optional store packaging
Bubblewrap or PWABuilder can wrap the same PWA for store listings when discoverability in a specific store outweighs the extra review overhead.
Apple’s constraint
An App Store submission of a PWA wrapper still goes through Apple’s standard review process and guidelines, unlike direct web installation.