I don't know if anyone has officially said so but there was a public statement about it being chosen as a reference to story telling (Celtic language). So could be for similar reasons or could be a reference. Not surprising considering how famous the story is and how famous Asimov is. But maybe someone else knows more definitively.
Here, I'll rephrase thenoblesunfish for clarity, because you seem to have misread
> Is this why the Google product (now just called Gemini) was called [Bard]?
"That" == "Bard".
They weren't referring to Gemini, which is why there's that whole thing in parentheses stating it's *now* called Gemini
From Wiki
| The technology was developed under the codename "Atlas", with the name "Bard" in reference to the Celtic term for a storyteller and chosen to "reflect the creative nature of the algorithm underneath".