That's the perfect usecase for like... a website.
In that regard, webapps work perfectly.
Bookmarks on the other hand are unbounded and suck to manage (no browser has improved meaningfully in this realm in ~20 years for some reason) so the threshold for what gets bookmarked is higher.
Some things are important enough for a bookmark, others are important enough for home screen.
If you go there infrequently, I don’t understand why you would clutter up any part of my phone - bookmarks or Home Screen - with its menu. If you go there frequently… you already know the menu?
For most places, but there are a handful that have huge menus. Its name escapes me but for instance when I lived in SF there was a sandwich place I frequented that was one such shop and aside from a couple of favorites I could never remember everything they had.
Also, these sites tend to facilitate ordering ahead, ordering delivery etc too so it’s not just a static HTML file.