I highly doubt, Bitwarden would initiate that. As far as I know, Bitwarden can’t even initiate that - it’s the OS or browser, I would think.
Which browser are you using?
As very recently discussed (Support "Device-Bound" Passkeys), this is something Bitwarden can’t do at the moment.
[Edit Aug 22, 2025:] The QR code “thing” is also something, Bitwarden can’t do at the moment (hence this open feature request: Support for passkey QR code usage via the mobile app on Android <14) As I now finally could test this with my Android phone, I see that CDA (Cross Device Authentication) is indeed possible with the Bitwarden mobile app, just like @dwbit wrote it in the thread @grb linked in his next post. [/Edit]
So, to me it seems, that Bitwarden doesn’t play a role in your issue… And I don’t know Chromebooks well enough, to be able to say anything else to that…
PS: Do you even see the Bitwarden passkey-window popping up? (like you can see here in the Help Sites) – That would indicate, Bitwarden would be involved…