I was just about to make this suggestion too. The share post menu automatically pops up in it's own tooltip, which explains what that is, but nothing happens on the bookmarks icon.
On the media pages the bookmark has no tooltip, but each share media company does.
As useful as icons are, and obvious that it is to us that it's a bookmark icon, until you know what it is, then it could mean anything. Icons and images are great, but some icons could have different meanings in different cultures. The bookmark icon is a bit of a weird one until you realise what it is, and a tooltip with a translatable phrase would be good.
Not having text for an icon is fine on the menu for alerts and messages, because experimenting with them only opens a drop down which can then be clicked off. Nothing of consequence is actually actioned apart from a UI change.
With those bookmark icons, it actually actions the saving of a post. So if you don't know what it is, the only way to figure it out is to click it, which actions something that needs to then be undone or deleted to return the previous state.
Because of that I think it makes sense is definitely of benefit to have to tooltip explainer on the bookmark icons.