This is an old chestnut that's no longer true. Safari's PWA support is better than Firefox's today, on both mobile and desktop. Two examples off the top of my head: Safari has better Web Push support, and supports the W3C's Badging API.
My impression for the last ~10+ years is that you could not depend on index db in safari, not for heavy use cases, and doubly so for ios and there was not a viable alternative whenever I checked.
I would be happy to know that things are looking better for PWAs on ios though if things are now viable.
Thanks for the additional background, I'll dig into that! FYI, based in part on our exchange, I created pwascore.com to scratch the itch of wanting a reasonably-objective "score" for browser PWA support.
