Warning… long post based on my understanding of the original concept for Traveller…
There is reason for jump space and x-boat systems.
When Traveller was first conceived, Mark Miller wanted it to be the wild west in space. He likened the 3 Imperium to “the pony express days of the Galaxy…” Mark wanted the “look and feel” of the mid-to late 1800’s with steam powered tramp freighters plying the far reaches of the world. It would take a weeks for a tramp freighter to travel from Europe to the far east, with many ports of call and adventure along the way… etc… Giving players the excitement and adventure and “grittiness” lost in a lot of the sci-fi settings of the time.
In concept, Traveller combined all these concepts set in the far future. (Star Trek was pitched as “Wagon Train to the stars”) for instance. I stopped playing Traveller in 1988-89 but picked it up again in 2000-2001. In that time there was a “shift” in the general fan base concept from “age of steam” to “age of sail”… why? Because transatlantic cables had already connected important cities by the mid-late 1800’s allowing telegraphs to send relatively instant communication, thus information delivered by ship (or horse) was a defunct idea… within the age of steam. True, rail systems and steam powered ships would carry messages and mail to cities and countries not yet “wired” to the early telegraph system, but instant communication was still in service during much of the age of steam.
But still Mark’s original concept persists within the core game mechanics. In fact the symbol of the x-boat service is a horse-like-thing…

So much for the short history as far as I’m aware of it… but I could always be wrong.
Back to the present, and your question.
Everyone before this post has done a great job describing why you cant send “energy/radio waves/meson communications” through jump space. I will only add one fine point. In jump space there MUST be a device continually maintaining the jump bubble. That device of course is the Jump Drive. The concept of Jump Space Travel within the Traveller game mechanics REQUIRE this. The ship, fuel tanks, power plant, (and people/cargo/computer messaging systems) etc… are simply along for the ride. Once the destination has been reached, the jump drive kicks in again, forcing the ship out of jump space, back into normal space as the jump bubble collapse. That’s why you can’t “beam” messages through Jump space.. or have “subspace communications” etc… there has to be a device to get you back into normal space.
IMTU I allow smaller frames than 100 tons (but not much) however the size of drives, power plants, etc… are based on 100 tons minimum. So a 60 ton hull would still require 10 tons of fuel for a jump 1, not 6 tons etc… (but these small ships are few and far between, not normally available on the open markets)
I forgot about the jump torpedoes… might have to revisit that again…
I did mention quantum entanglement ages ago on another thread, without much support… lol
But if you like that idea, perhaps quantum entangled communications systems can link sector capitals to sector capitals for instance, the use normal x-boats to disseminate important messages throughout the rest of the sector. I’ve no idea how these quantum entangled communication systems would work or the costs, but it would be more than a loaf of bread…

IF you like that idea, the quantum-entangled communication systems could be analogous transoceanic cables. Thus, if you so chose, you can finally bring Marks original concept of future/sci-fi version of life, travel, and adventure in late 1800’s, into reality.
Jak