In colloquial usage "zooming in" on something is to make it appear closer or larger. In technical terms, this is represented by the focal length. Your confusion comes from expecting the zoom ratio (the "times zoom") number to represent the amount of zoom in the colloquial sense, when in photography we use it simply in its technical sense: the amount any individual lens can change its focal length. This means you are focusing on the wrong number.

The thing you are looking for seems perfectly reasonable; it just happens that terminology evolved in a different direction.

In reading your comments, I think that you're also actually still misunderstanding what the times-zoom number for a zoom lens means. That is, it seems like you think that it represents magnification in some way. That's a logical assumption, but it's just wrong. That is, I know you understand the calculation outlined in How do I convert lens focal length (mm) to x-times optical zoom?, but I think you're misunderstanding what the result actually means.

It sounds to me like you assume that the number you get by dividing the higher focal length by the lower focal length tells you the magnification, or "how much zoomed in the lens will be". This is not the case. A zoom lens can vary the focal length, and the given numbers represent the range by which it can vary. But at any specific setting, the size of a distance object will be the same. That is, if one lens goes from 70-200mm and another goes from 100-500mm, if you set either one to 200mm, the resulting image will be the same (give or take other differences in the lens). In fact, if you have a non-zoom prime lens which is fixed at 200mm, it too will show the same image.

So:

Except when considering the very-close-up macro situation (which is covered at What does the magnification ratio number mean on a macro lens?), the only important number here is the focal length, which determines the angle of view. The smaller the angle of view, the larger far away things will appear — and, the larger the focal length, the smaller the angle of view. If you are concerned with how much "reach" you have, all you care about is the larger number given for a zoom lens.

There is no standard "base zoom" number — as you've figured out, and as explained in How do I convert lens focal length (mm) to x-times optical zoom?, it just the ratio of a lens's extreme focal lengths.

If you're looking to compare different lenses for the amount of reach they have, looking at the times-zoom number doesn't tell you much. However, comparing 210mm and 1300mm does tell you something. Don't worry about the amount that each lens's focal length can change (the zoom) and just look at the focal length number.

You can use a field of view calculator (there are many on the web, plus lots of apps) to figure out what this will mean in practical use, but you can also take advantage of the simple formula here: How to calculate the new field of view from an existent one?. 1300mm is about 6× 210mm, and so if you take a picture of the same object with both, it will appear about 6× larger (in each dimension) with the 1300mm lens.

Be aware that this is only relevant when the sensor size is the same. If your sensor (or film) is a different size, you have to take that into account too. See What is crop factor and how does it relate to focal length? for more. This is why the idea of "35mm equivalent" was invented — it normalizes the numbers to one standard so they can be compared.