But what exactly?

Wikipedia says it does support it https://en.m.wikipedia.org/wiki/Progressive_web_application:

And I know I’ve written Progressive apps for iOS myself - manifests etc.

So I know it’s not as simple as you’re saying. What do you really mean?

Safari absolutely does not support PWAs in a meaningful way when compared with other platforms. Service Worker support is fine, but one of its main features is its use in combination with the Push API, which is not supported in Safari. This omitted feature alone alone makes web apps on iOS far less valuable than native apps. There are other omissions as well, but this one in the most glaring.