They used to make digitizer modules for analog scopes, such as this:
https://w140.com/tekwiki/wiki/5D10Some analog scopes have this functionality built in too. They look like analog scopes with analog dials and all, but they have some digital brains in there that gives you some digital functionality like on screen cursors or capturing a waveform and downloading it digitally over GPIB. The reason for this hybrid analog+digital aproach was that digital electronics and data converters ware not fast enough to work with these fast high bandwidth analog signals that analog scopes could show.
So these scopes combined the best parts of analog and digital together. The cursors got drawn to the screen as a "3rd channel" operating in X Y mode by a CPU. The capture functionality typically only worked at very low sample rates like 0.1MSPS because that's what the common ADCs of the time could do. Or the scope would have a CCD chip that works as a analog shift register to record the waveform as a series of analog buckets of charge that then get cycled around to be read by the ADC at a slower rate, or shown on the screen. This was a big thing because it gave single shot recording functionality.
With a webcam you won't be able to get this single shot capture ability out of a analog scope because the image will be likely way too dim at any sort of high sweep speeds. While at slow sweep speeds you could use a MCU with a built in ADC to digitize it.
Electronics have progressed a lot since the 80s, so today such a digital plugin could be made for probably 50 to 100$ in as a small 5x5cm board holding a fast ADC/DAC, FPGA, MCU that you can wire in between the analog channels and the CRT electronics to capture signals and draw then to the screen. But its easier to just buy a digital scope these days.