> My impression was that teletypes were the first proper keyboard-based interfaces.

They (about) were, AFAIK, but using them with computers wasn’t their first usage.

https://en.wikipedia.org/wiki/Teleprinter:

“A teleprinter (teletypewriter, teletype or TTY) is an electromechanical device used to send and receive typed messages through various communications channels

[…]

Initially, from 1887 at the earliest, teleprinters were used in telegraphy. Electrical telegraphy had been developed decades earlier in the late 1830s and 1840s, then using simpler Morse key equipment and telegraph operators

[…]

With the development of early computers in the 1950s, teleprinters were adapted to allow typed data to be sent to a computer”

Even for that, there was prior art. https://en.wikipedia.org/wiki/Printing_telegraph, which used a piano-style keyboard.

The Linotype also is quite old. https://en.wikipedia.org/wiki/Linotype_machine:

“The Linotype machine operator types text on a 90-character keyboard.

[…]

In July, 1886, the first commercially used Linotype was installed in the printing office of the New York Tribune.”

Mechanical typewriters have different physical mechanisms to feed forward a line or make the carriage return. I think it doesn't turtle much further back than that.

The telegraph was keybased - only one key so I can't call it a keyboard, but in other ways it is what you are asking about.