Does Kubera have access to my online bank account?

No. Kubera DOES NOT have your banking or crypto account credentials.

Kubera uses third party financial account aggregator services like Plaid, Mastercard, Yodlee and MX to connect to your accounts. They are market leaders in financial data aggregation services used by leading FinTech innovators and financial institutions worldwide. They adhere to industry leading practices for data security, regulatory compliance, and privacy.

Your banking credentials are directly sent to the respective service provider from your browser. Kubera servers will never see your credentials.

Kubera CANNOT move your money.

The account aggregators provide a read-only interface to Kubera; therefore Kubera cannot make any transactions on your behalf.

More details https://www.kubera.com/blog/bank-investment-portfolio-auto-update

Most of your security related questions are answered here in simple English https://www.kubera.com/security