Yes i suspect D'Addario and Kalium also just carefully measure the unit weight, then use that and scale and pitch in the equation to get tension.
To go into deeper detail, that string equation is based on an assumption of a 'perfect string' with zero stiffness.
However no need to be alarmed by this as bass strings are actually, in terms of this assumption, very flexible, their stiffness has a quite insignificant effect on the tension result.
If you think about how wobbly a bass string is when you dangle it from your hand, and how easy it is to bend very slightly in your hands, there is almost no resistance. Compare this resistance to the huge tension that is applied when on the instrument, it is fairly insignificant.
How a linear object vibrates depends on its tension and its stiffness and the balance of those.
At one extreme is a vibraphone with zero tension and high stiffness (solid metal bars), when struck the 'restoring force' acting against the deformation of the bar is entirely due to stiffness.
The frequencies of the harmonics are very different from those of a guitar string.
At the other extreme is guitars with very low stiffness and high tension, when struck the 'restoring force' acting against the deformation of the string is almost entirely due to tension.
The frequencies of the harmonics are what we consider 'harmonic', being 1x 2x 3x 4x 5x ... the fundamental frequency.
So what is the effect of stiffness on the tension of a (bass)guitar string?
Stiffness acts as additional 'restoring force' and therefore raises pitch. To return to the desired pitch you then have to reduce tension a little. So the actual tension at desired pitch is a slightly lower than the result of the basic equation, but not by a significant amount and not enough to be bothered with when calculating tensions. Scientific equipment to accurately measure stiffness is rare and expensive, whereas unit weight just requires an accurate weighing machine, weigh 34" of string and divide by 34.
Stiffness in a guitar string also shifts the frequencies of the harmonics, causing 'inharmonicity', that 'out of tune with itself' tone you get when playing a B or E string on the highest frets. Playing a fat string on the high frets effectively raises the stiffness, and therefore pitch, meaning the scale length needs to be increased to acheive the desired pitch, this is why we offset the saddle position away from the nut to intonate a string, and the offset is larger for stiffer strings. As you play up the frets the intonation offset becomes larger relative to the length of the string, to provide an increasing compensation.
