or are there some weird historical archives full of video's of segment displays?
Back in the olden days of hardware RSA tokens, there were stories of people bridging out the TOTP values via setups like this. I've got an amplifier in the garage hooked up to a smart outlet that'll turn it on, but I have to go over there manually and rotate the knob from 20db to 50db.
I've been tempted to hack up some sort of "RC-Car Wheel + WebCam" to be able to remotely control/nudge the volume, but luckily my lack of free time prevents me from going off the rails like that. My other option is some sort of arduino and hacking at the rotary encoder circuit directly from the inside, but again (luckily) my lack of free time has kept the box closed.
The world's bigger than what you've seen so far, I'm guessing!
If one doesn't have free time, consider half the budget for the RPi+camera, then just find the closest makerspace or kid with an interest in electronics and ask them if they would like to hook it up for you, you saved half your expense, the kid has some more experience and some money to show for it.
Same with the amplifier knob, just needs a cheap wireless microcontroller, and sufficient low pass filtering on a PWM signal, perhaps a quad op-amp IC for the filtering and the voltage buffer...