Is it possible to have an universal RF receiver and transmitter (Wifi / Bluetooth)
Practically speaking, no.

Theoretically yes, but it gets tricky.

If you only needed to do one way communication, you could build a pure-analog system which would just receive a chunk of the 2.4 GHz band, amplify it without caring to understand the detail, shove it down a suitable transmission line, and push it out an antenna at the other end.

The problem is that most of your devices are bidirectional.  If they were bidirectional with a range of frequencies reserved in each direction, you could use two instances of same trick as above, with careful filtering to separate the upstairs vs. downstairs frequency ranges and avoid looping feedback signals through the system.

But that's not how these services mostly work - they are bidirectional on the same frequencies, taking turns in time (or at least the transmit and receive channels are intermixed).  To relay this requires something that actually understands the protocols of all the services involved.  In theory, a sufficiently smart software defined radio could receive the entire band, process all transmissions for all known protocols, decide which should be repeated upstairs or downstairs, and send that over a cable for its partner in the other location to re-transmit.

In practice, this is too complicated.  You are better off using existing per-protocol solutions.  For example, you can get wifi hotspots that are designed to work together, interconnected by an ethernet cable, and route traffic between their respective peers.  

Bluetooth repeaters seem conceptually a bit trickier, but might exist.

Ultimately, the possibility of buying these off the shelf is not a question that would be on topic here; what I have tried to do is give you an engineering answer as to why a universal system would be hard to build yourself, and why it is probably not on the market.