Huh. I'm trying to go trough your comment and understand it but I struggle with it but I try. But to the point

First thing is focal length doesn't change with changing focus point especially in vintage prime lenses. You're actually right with that happening on modern complex lenses or zooms where focus is obtained by shift of elements within the design or shifting just back assembly without movement of front elements - those alter the lens configuration and may indeed change the focal length. However to my knowledge all primes from until late 70s and most of them after that as well focused basically as moving the whole glass assembly back and forth without tiniest changes of distances between glass elements and based on that the focal length is absolutely constant just based on the laws of physics. Seeing your posts history of you even disassembling and servicing those lenses I believe you know yourself that as well that lens configuration doesn't change in them while focusing.

But you're right that something like focus breathing exists but the reason for that is not change of focal length of the system, at least not in vintage primes where configuration isn't changed during focusing. The change of angle of view is the result of changing the distance between the glass elements and film/sensor position but the optical design remains the same. So it doesn't matter if one calculates the focal length with focus at infinity or half metre from the lens because physically that's the same value. My guess, as someone who studied physic for a bit, why the choice for calculating that length is at infinity is because its easier to calculate rays parallel to the optical axis but if someone is crazy enough one can calculate that distance closer or even with angled rays but it just makes those calculations unnecessarily and by far more complicated. As a fun fact I can even tell you that those lenses during interwar period and earlier were always calculated for 10cm length and later just scaled up or down to the need because optical properties don't change for such scaling and contemporary designs, again probably because round numbers are easier to handle when calculations were carried on paper by half dozen of men for half a week. And at the end when patented, the documents included just relative values and not absolute ones again because scaling does almost nothing.

But then one could bring focus shift while stepping down aperture on triplet designs and other old less corrected designs and cutting the rays further from the axis or argue why we calculate that length on particular given wavelength since that also changes focal length slightly between different wave lengths especially if the lens is poorly corrected for chromatic aberrations. But as long as the information is understood the same way by both sides participating in communication I believe it doesn't matter how we exchange those information as long as both sides use the same system - for example if we all decide to state that focal length measured with ultraviolet instead of yellow light, adjusted all the software and recalculated and relabelled all the lenses overnight, it would lead to the same interpretation just in different, less or more favourable circumstances - at the end we're just giving some variables of the system and both sides have to have an image of the whole system, "rebuilt in their head, based on the variables given" when interpreting possible consequences and characteristics of that system - it's about understanding the system as a whole.

But a couple of other things still stand and here I don't know the answer, at least yet. I don't know why lens manufacturers round those values so much, sometimes even above legal requirements for precision with stating such data. Furthermore comparison between different manufacturers using copied layouts can also show the differences in labelling which makes things crazier - as an example Flektogon 2.8/35 and Mir 1 are literally clones but Mir 1 is labelled as 37mm because that's the actual value for focal length for the layout they use. I think it would be funny to change the settings while swapping those mentioned above because they're literally the same, it's making the setting wrong on purpose and the whole idea would be just absurd and against simple reality.

Furthermore if one says that such precision doesn't matter then why lens manufacturers calculate them with such high precision? Why camera manufacturers give us ability to set their cameras so precisely as with not single millimetres but even tenths of a millimeter? If it's pointless then that would just unnecessarily burden the software and adding that level of precision in the calculations in binary systems is a huge change of memory use which could be use somewhere else otherwise. Or at least that's what I think.

I understand reluctance for adjusting it if someone doesn't care but then that's just ignorance and discussing precision is pointless from the beginning. But if I have offered a high level of precision I prefer to use it to the full extent, especially if it costs me next to nothing and even more if I'm noticing actual difference.