Might be a good product to app-ify. Maybe a USB dongle that acts like a keyboard and controlled by your phone. Give it some sort of 1Password / Bitwarden integration.

Could make it double as a YubiKey.

Surely this exists already?

Yubikey supports this already, but without the phone part.

Does it require installing 3rd party software on the host machine? This might not work great for this kind of "shadow IT" application in all environments, whereas one that acts as a USB keyboard might be more versatile.

Does it require installing 3rd party software on the host machine?

No, it identifies as a keyboard. It also defaults to generating a password that will use the same scancodes on (most?) western keyboard layouts so that computers configured to default to e.g. QWERTZ or AZERTY will still result in the same password.

How do you tell it which password to type?

IIRC there is a maximum of two; one on short-press and one on long-press.

Only to configure it. It presents as a USB keyboard (among other device types).

How do you tell it which password to type? I haven't seen yubikeys with physical interfaces to select a particular password.

I should do this for ssh password entry. Running ssh-agent is still 90% of the story, but it comes up often enough that I'm on a terminal in a remote machine or inside a screen session or something that it would still be awfully useful to be able to just autotype it.

Separately from the password aspect, consider how convenient it may be to use your smartphone as a kind of re-reified "clipboard": Use the camera and on-device OCR to copy text, then "paste" it as a virtual keyboard connected over USB.

It's very niche, but in those rare situations it'll be a big time-saver compared to human transcription or the rigamarole of setting up some other kind of data channel.

Now I’m curious if BT can be secure enough for all this (responsibly)

The InputStick¹ can provide the hardware side, the software side is open-source² as well. It only has a keepass2android plugin at the moment though.

1: http://inputstick.com

2: https://github.com/inputstick

Yubikeys can do this.

It can, and I tried this, but in practice we have to change our passwords at my current employer so frequently that I got more irked changing it on the Yubikey (not the least hassle-free of processes, as I couldn't install the Yubikey software on the work machine) than just typing the thing.