Interesting that it shares a root with a completely unrelated word. I expect that the word ענב as tie is relatively recent whereas ענב as grape is biblical, yes? So why choose a word for tie that's already in use and has been for thousands of years?
Are there other examples of unrelated words with the same שורש?
It's what homographs are all about. Though they are less common in Hebrew than in English.
Grape ענב is biblical, tie ענב is talmudic at least.
Some examples (though nikkud does differ)
Book and barber are both ספר.
Ice and bald are both קרח.
Evening and guarantor are ערב
In the examples you have the nikkud differs between forms so these examples are homographs. In the case of ענב the nikkud also differs but doesn't change the pronunciation so this is a homonym. At least according to http://www-personal.umich.edu/~cellis/heteronym.html
I expect that Hebrew has a fair number of homographs but far fewer homonyms, yes?