Radios
As a natural consequence of some of the contents of my omake, we're probably not far off from radio equipment that could survive a tank's vibrational environment and the kind of jars it might get from gunfire and uneven terrain. The bigger issues are power and an antenna.
On the power side of things, it is perfectly possible to do radio communications with what batteries of the era could realistically put out. Look up "QRP" sometime. These days, hams do that sort of thing as a challenge and can sometimes even achieve intercontinental ranges with luck, skill and a good antenna. Back in the tech level we are dealing with, though, the equivalent is radio sets made from a design from a magazine and built in a shed or something with a range in at most the low tens of miles and more likely quite a bit less I would think. For substantial range, you need more power than that. Power that a tank engine could in principle provide, but there's no way the relevant equipment is going in our standard tank. Receivers, on the other hand, take no power at all: at this tech level, using vacuum tubes to make receivers more sensitive than a crystal radio is maybe just starting to be experimented with. We've got an advantage in having something on the path towards being a modern diode to work with, but that's a bigger deal for reliability than it is for sensitivity. It's also worth noting that that type of "detector" is good enough for AM voice, which should be in the earliest experimentation at this stage but won't be practical for quite some time.
Antennas: First of all, understand that antennas need to be a substantial fraction of the wavelengths they are meant to work with if they are going to work very well. There are tricks you can use to help with this, but many haven't been invented yet and they only work so well. Next, understand that at this tech level, "shortwave" and "high frequency" were entirely unironic terms, rather than referring to the longest wavelengths anyone would think to use for things other than talking to submarines. 80 meters or so might be around the practical limit, and the wavelengths people are mostly using will be well over 200. With that in mind, an antenna permanently mounted on a tank is probably a non-starter, and some kind of mast that could be raised as needed is at best a huge technological achievement that would involve hours of setup time and one or more wagons to carry the pieces. What we're realistically left with is wire antennas that can be hung from trees, buildings and the like, or maybe even anchored to a kite or balloon for a vertical antenna. It should also be noted that vertical antennas need a good ground, which a tank may or may not adequately provide, while a wire dipole can do without.
With all that in mind, we can't possibly put a radio on a tank for use in combat, and putting a radio transmitter on a tank that can be used while parked would require either a very specialized variant and more room inside than we can reasonably expect to have, or a short range transmitter carried in one or more large boxes stowed externally. However, a receiver that can be used while parked with a bit of setup time is actually not too hard if we've got a little room for it, and a specialized radio vehicle should be possible if we had a use for it and the time and money to throw at it.
People who know more than me about our actual needs can make of all this whatever they like.
Here's a resource on the sort of things you can do with compact equipment and battery power at this tech level. We can replace the coherer (figure 4) with a rudimentary diode, but otherwise this isn't far off from what the system we end up with might look like. If I'm reading it right, they even seem to be using a copper plate as something like a capacitance hat for their antenna to let them get decent results with a shorter length than would otherwise be necessary, though they don't seem to have any idea that that's how it actually works. We could probably do something like that to keep antenna length somewhat manageable.
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