It's probably best to wait until the UI actually tells you Bard has been updated to Gemini Pro. Previous Bard updates have had UI announcements so I'd guess (but don't know for sure) that this would have similar.
> Bard with Gemini Pro is rolling out today in English for 170 countries/territories, with UK and European availability “in the near future.” Initially, Gemini Pro will power text-based prompts, with support for “other modalities coming soon.”
I'm biased here, but based on my general engineering experience I wouldn't expect it to be about privacy/data protection. As a user I think things like Wipeout/Takeout, which have existed for a long time, show that Google takes this stuff seriously.