So CAV (constant angular velocity) is an encoding format for laser disks. When something is written with CAV, it is basically analogue data and therefore repeating patterns can be recognized on the disk.

No, CAV has nothing to do with encoding, and both analog and digital formats have used both CAV and CLV and hybrids of the two.

The legible text seen in the microscope images happens because of the combination of LaserDisc recording a raw and uncompressed encoding of the analog video signal, the way that LaserDisc used CAV to store an integer number of frames per track so that the image data for corresponding on-screen locations of subsequent frames would be aligned at the same radial position on the disc, and the credits scrolling vertically at constant speed.

If LaserDisc had used a digital encoding (especially a compressed encoding), the data on disc may still have had discernible patterns but the text would not necessarily have been legible. If it had used CAV but not stored a whole number of frames per track, then temporal and spatial locality on screen would not have corresponded so well to spatial locality on disc. And the vertically-scrolling credits are pretty much the only kind of content that can produce the recognizable and legible images on the disc surface.

I think the fact that the aspect ratio of the text came out approximately right probably is a consequence of the scrolling speed of the credits being chosen to suit the vertical resolution of the video. If the text had appeared squished in the microscope, it would probably have been moving too fast on screen to be clearly legible.

Is the image seen via microscope basically a readout of the image on a spectroscope?

Those can have near-legible images, but most of the time they are not.

No; it's strictly a reference to constant RPM or variable RPM.

CAV discs contained one frame per rotation. While this meant you could only fit half an hour on one side of a disc, it did give you perfect slow-motion and freeze-frames.

I worked in a video store and loved LaserDiscs. The Duran Duran video album was CAV, and the Pioneer LD-700 had such a fast transport mechanism and remote control that I could to DJ-style "scratching" with it.

Not simply repeating patterns, readable text from the credits as shown in the video.

Here's where the text comes into focus, pretty cool:

https://youtu.be/qZuR-772cks?t=1540

Sorta?

The data being written to the disk is the same in CAV or CLV disks, but the player just needs to know how to spin the disk at the right speed so that the laser can read the pits/lands correctly. It is purely a detail about the speed that the disk is spun at so they can cram more data on it with CLV disks.

What CAV LaserDiscs allow for, though, is to make it extremely obvious where scanlines and blanking intervals are in the video signal.