I never wrote that EDID is for error correction- it's part of the 'handshake'- if it doesn't meet the requirements, we're not going to see video or hear the audio, or both. It's used to identify the device characteristics, so one piece will know how to send the signal (resolution, aspect ratio, etc).
Analog vs digital has NOTHING to do with the disc being stamped into aluminum! NOTHING! You're trying to make one definition of 'analog' apply to the physical disc when everyone else is using 'analog' or 'digital' when referring to the signal. You might want to use 'tangible' when referring to the disc.
An analog signal is continuously variable, with no breaks in, for lack of a better term, the waveform. Can it have sections where no variation occurs? Of course- that's part of being variable. Maybe the stream of information is better. Digital SIGNAL is discrete pieces of information that are assembled in groups of bits that have some meaning (again, binary digits, which are either ones or zeros, on or off), called 'words', in a way that they can be read by the converter and re-made into an analog signal, as it impacted the mics or entered the mixer from the electronic instruments. Morse code is groups of light flashes, dashes and dots, short and long 'pings' of sound, that have meaning. A continuous string of these dots and dashes, etc can be assembled but without pauses between the words, it takes longer to decipher the message. Jumble them together and it's jibberish
unless some kind of pre-determined key is used in the event that the order of the words is changed, possibly to prevent others using the information. CDs use 16 bit encoding of signal that was sampled 44.1KHz (actually, 44,056) times per second. DATA from each frame is distributed throughout the disc, but the disc in Orange Book is limited to 99 separate tracks and that precludes randomly placed data.
PCM recording on tape uses/used 14 OR 16 bit- if 16 bit was used, S/N was better but there was no data for error correction and if 14 bit was used, two bits were available, called 'parity bits'. If you look at the video from a PCM recorder, you would see columns of lines that vary with the signal content, separated by a thin gap of noise and at 14 bit- two columns are seen at the right side, neither with the same density of activity, mostly dark. These are used for error correction and it's not a fixed frame- it, too, changes with the signal.
If you break up the data on a CD in the middle of each word and jumble it all together, will it come out as music? No, it won't. Why? Because it wasn't intended to be placed on the disc, randomly. That's how data is stored on a hard drive, but that was too expensive to use at when CDs were developed and scanning from the center to the outside of a disc (linear scanning) was an easier proposition. However, that method doesn't make it 'analog'. The first Sony CD player retailed for $900- a hard drive at the time was far more more expensive.
You, yourself, wrote that the data is stored in digital form and must be converted to analog- again, it's not the medium that makes a CD digital or an LP analog- being read with light makes digital storage possible but a stylus in a groove can't track high speed data as anything close to square waves, on/off pulses. At a slow speed, with some way to prevent the stylus being damaged, it's definitely possible to store a digital signal on a disc that needs physical contact to be read at a slow speed.
https://www.philips.com/a-w/research/technologies/cd/technology.html
Here's a link to info about the Reed-Solomon Cross-interleaved Coding-
https://www.usna.edu/Users/math/wdj/_files/documents/reed-sol.htm