Once again, you are wrong. The diagnostic equipment and beam testing procedures that I suggested you read clearly show that the magnetic field outside a beam of charged particles is identical to that outside a wire.
In a particle accelerator, one can compare the current with these magnetic sensors to the current that hits a Faraday cup (which suppresses the effect of secondary emission from the target).
Have you ever seen a particle accelerator, or read anything about them?
What do your countrymen at the Australian Synchrotron Lab say?
PS: doing some elementary Googling, I found an interesting engineering thesis from Georgia Tech back in 1962: https://smartech.gatech.edu/bitstream/handle/1853/14924/lineberger_william_c_196212_ms_69818.pdf?sequence=3&isAllowed=y
The author discusses practical methods for measuring the magnetic field induced by a beam of charged particles without interrupting the beam. Since this was already a physical phenomenon applied to practice in engineering, no one needed to crow about it.
But, if the magnetic field of a steady DC electron beam in vacuo (in a glass tube) is equal to the magnetic field of the wire supplying the steady DC, then this falsifies the STR explanation (ie that it is due to the length contraction of the wire), because there is no wire for the electron beam, there is only vacuum.
The vacuum contains spacetime, & i suppose that Einsteinists could claim that the space of the spacetime contracts, but that would i think require that the electrons spacings also contract, which would give the beam a double dose of negative charge, which is the opposite of what Einsteinists are looking for.
Your logic here is fallacious.
1. It is well-established experimentally that current through a wire and current in a beam of charged particles induce a magnetic field
B, according to the law of Biot and Savart that is later incorporated into Maxwell's Equations.
2. Purcell published an explanation for a
particular common case of current flowing through a metallic conductor, where the substantial magnetic field is induced despite the wire being electrically neutral. There is some controversy about his derivation, some of which suggests that it is only useful as a pedagogical explanation. However, quantitatively, it agrees with experiment. He did not discuss this as an explanation for other situations of current, although he does say elsewhere in his textbook that there are other forms of current besides that in a wire.
3. The case of a charged particle beam is a different configuration, since the beam itself is not electrically neutral and the velocity can easily be "relativistic" or "very relativistic" for an electron beam at a reasonable kinetic energy, while the drift velocity in Purcell's explanation is not so large.
4. The experimental evidence for case 3 does not refute case 2, since the basic situations are different but the current is the same.
I can make fun of your logic with this analogy:
1. Visible light is that portion of the electromagnetic spectrum that can be sensed by human vision.
2. A common source of visible light is an incandescent light bulb, where current through the filament heats it to incandescence and much of the electromagnetic radiation emitted by the hot filament is visible.
3. Another source of visible light is bioluminesence, produced by chemical processes within a living organism. There is no external source of electricity to the firefly, and the firefly is not heated to incandescent temperatures.
4. The experimental evidence of case 3 does not mean that case 2 does not emit visible light.
Note that one form of bioluminesence is "foxfire" in forest fungi. I could claim that it was named in my honor, but it probably comes from the French "faux" for false. An interesting coincidence is that the same phenomenon is named after foxes ("kitsunebi") in Japanese folklore. See the Hiroshige print "New Year's Eve Foxfires at the Changing Tree, Oji, No. 118 from One Hundred Famous Views of Edo"
https://www.brooklynmuseum.org/opencollection/objects/121730I tried to obtain a copy of this print, but had to settle for a museum-quality reproduction.