And yet, it says "save" right there on the button.
Don't miss the larger point: "save" no longer means what "save to a floppy" used to mean. For a lot of people, "save" means to download, or to bookmark, while apps do the old "keep app data for later" by themselves in the background.
The image is of a website and the context is "save your place", which is why it's a bookmark icon: that button creates a bookmark that loads that page back up. The context here never meant "save to a floppy".
It's 2023, there is no context anymore for "save to a floppy". As for the "Save" like in the meme, the contexts we have left nowadays are: "save your place", "save to your device", "export", and little more. In fact the "Share" icon could replace them all, with "Share" on mobile showing, among others, options like "share with the cloud app" or "share with the file explorer app".
I think "save to local storage", (be it a floppy, a HDD, a SDD or whatever NVS phones use) is a timeless context that isn't going anywhere. Share, implies lending access to someone else, it is a completely different concept than save.
I'd argue that mobile apps have been trying really hard to make the "local storage" concept go away: auto-save, cloud as the canonical storage, transparently managed local caches... and the user needs not care about where their data is at any moment: it's "in the app".
From that point of view, "save to local storage" makes sense to become a "share with the app that happens to save to local storage"... but that could also be any other app which would keep the content for later use, not necessarily on local storage.
If anything, over time we might see the emergence of a "move the content" context, from one app to another, in addition to "share the content".