You can paste the URL or an identifier (e.g., DOI) into the save page [1], or even create an iOS shortcut that encodes the current URL into the 'q' parameter for that page.
Historically the solution was to use the bookmarklet [2], but you might need to disable "Prevent Cross-Site Tracking" in the Safari settings for that to work reliably.
But yes, the beta iOS app [3] supports full saving of metadata and PDFs via the Share sheet.
(Disclosure: Zotero dev)
[1] https://www.zotero.org/save