Can the horizontal menu have tooltips for each item?

I have a horizontal menu with three items and I'd like to add a tool tip for each one but it appears there's only a tool tip available for the entire menu?

I tried manually adding the object into the item but it appears to ignore it, along with some error messages about it not being supported in the schema.
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The docs for the component do not show any form of per-item tooltip support:

I cannot recall an instance where a "not defined in the schema" error was inaccurate as to any specific functionality.

Sorry.

Perhaps you should add a feature request to the ideas site.