To be clear, Brave is built using the Chromium engine — which is inherently different from the actual “Chrome” web browser. Many browsers user Chromium as the underlying engine — including (but not limited to) MS Edge, Vivaldi, Opera, Arc browser, Kiwi browser, just to name a few.
Please note that even though we use the Chromium engine, Brave sifts through the Chromium code to ensure that your privacy remains intact but stopping out any telemetry and/or communication with Google or its servers.
We have a page that documents exactly what we remove from Chromium before pushing any updates to Brave here:
@Dee-F,
In short, your bank showed that you logged in via “Chromium” because that is the way Brave is detected by many websites due to it using this engine. However, your banking is secure and has nothing to do with Google outside of what was mentioned.
Hope this helps.