How does a screen work?

I have to take issue with the usage of the terms "pixel" and "subpixel" with regards to CRT. CRTs do not display discrete pixels. They display discrete scanlines, each one made up of a smoothly varying voltage across the line (and thus resolution is a function of both the DAC in the display device in the case of systems that generate a digital signal and then convert it to analog for display, and the hardware inside the CRT monitor). Also, there is no mapping between any "pixels" represented within that varying voltage and the separate color phosphor dots.

Even "digital RGB" isn't digital in terms of the CRT. It's only "digital" because each color channel has a nominal on and off voltage, with no in-between (outside of the separate intensity pin). However, the electron gun still has a rise and fall time that is not instant.

Displays didn't truly become digital for the masses until the LCD era, with DVI and HDMI signals. Even analog HD CRTs could accept these digital signals and display them.

I don't think this is an entirely fair characterization either. Note that everything I lay out here is just based on accumulated information gathered over the years due to vague interest, I haven't worked on or with CRTs (did use them though).

Monochromatic CRTs were well and truly resolution agnostic, there were legitimately no pixels or subpixels or anything similar to speak of. That said, the driving signal still had to be modulated to produce an image, and so it's not magic either. You can conceivably represent [0] all the available information in them using just 720 samples per line, which is exactly why DVDs had that as their horizontal resolution (720 pixels).

This story changes a bit though with color CRTs, where you did have discrete sets of patches of different phosphor chemistries called triads. There was absolutely a fixed number of them on a glass, so you could conceivably consider that as the native resolution for that given display, with each triad being a pixel, and each patch being a subpixel. The distance between these was the aperture pitch, much like how you have a pixel pitch on a typical flatpanel display.

The kicker then is that as you say, there's no strict addressing. From what I understand there were multiple electron guns scanning across the screen simultaneously, only being able to hit the specific color they were assigned, but the patch they were hitting wasn't addressed, they just scanned across the screen like the single electron gun did in monochromatic CRTs. You'd then get resolution invariance by just the natural emission spread providing you with oversampling / undersampling without any kind of digital computational effort. It's not really true resolution independence like with the monochrome ones, I'd say. I even recall articles where they were testing freshly released CRT monitors, and discussing how sharp the beam was, resulting in what kind of resolution adherence.

[0] an earlier version of this comment said "extract from" here; for various reasons you might already know, that's a different thing, and would not actually be true.