I'll assume you're being hyperbolical. By all measurements the latest Safari, whether on the desktop or mobile device, is as "modern" a browser as any of the others.
I frequently build PWAs, and see no more friction building a PWA using Safari on iOS/iPadOS than I do for Chrome on Android.
That said, the reason the OP's site doesn't work in Safari has nothing to do with whether or not Apple supports PWAs or not.
I wish I could say the same. Even getting a complex SVG to render correctly can be a pain, and WEBGL / WebP support is non existent. It’s been awhile though, perhaps I should take another look at the updates they’ve made since.
I frequently build PWAs, and see no more friction building a PWA using Safari on iOS/iPadOS than I do for Chrome on Android.
That said, the reason the OP's site doesn't work in Safari has nothing to do with whether or not Apple supports PWAs or not.