Well, there is a trade-off between privacy and convenience in this case.
Sounds like your best solutions would be:
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Make sure that your vault is unlocked before using Visio (and that the vault time-out option is longer than the Visio session).
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Temporarily disable screen sharing in Visio while unlocking Bitwarden.
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Connect a second monitor (that is not used for screen sharing in Visio), and use the second monitor to unlock the browser extension — you can open a second instance of the browser for this purpose.
Also, you may want to vote for the Feature Request Credit card autofill using hotkey or on page load , since this would allow you to retain the convenience of credit card autofilling, while also using the privacy option of hiding the credit card information from the “Tab” view.