The jansky (symbol Jy, plural janskys) is a non-SI unit of spectral flux density, or spectral irradiance, used especially in radio astronomy. It is equivalent to 10e−26 watts per square metre per hertz.
It all in some complicated relationships with other stuff, funny and with pictures https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/sensitivity
Which also includes exposure, which defines bitrate as well, and defines detection range.
Looking at Radio telescope sensitivity calculator and understanding not so much from it, but having some fantasy and gaming expirience from playing with it, totally ignoring antenna gain, and just taking System Equivalent Flux Density (Jy) == 1743Jy, which I understood as antenna own noise it has at 50K etc.
We probably ready to estimate lower limit for signal detection, but warranty is void at inception.
Energy required to arrive to a detector looks like 3e-23 W/m2/Hz (that Hz thing is not that important for our estimations it can be 100MHz band or monohromatic source, things are not necessarily that simple there but let's ignore for simplicity)
So omnidirectionl source emitter should be about 1e20 W, if a reciever is 1m2 antenna. So bigger antenna can slash the number proportionally to its area, 1km2 as an example, maybe by 6 orders of magnitude. A dyson worthy big one, 10'000'000 km square, probably can slash it down to a 1W, eh.
If it is a more directional emitter, it also can help reduce power requirements, getting there 4 orders magnitude reduction is reasonable enough with usual phase array, and more with some laser based solutions, but there will be limits defined by all kinds of factors.
Bitrate also affects required power, but it hard for me to tell, but for current numbers, as it defined as detection with 1s exposure(which comes from watts in Jy), it seems that number has to be multiplied by desired bit rate, but I can be wrong about that.
So 1MW emitter, 10'000 by 10'000 km reciever, modem bit rate from 90's can be a valid setup, for directional connection. And few GW's for omidirectional signal.
Hm, seems someone needs to make bigger antennas, eh, because it seems if we need to waste more than few GW's they aren't worthy to listen to our radio station with best hits from 60'000 BCE