What is the smallest component to send HTTP requests on the Internet?
Since product recommendation questions are off-topic, I'll answer the underlying question of


  How small could a fully functional 2G/3G/4G module possibly become?


The answer to that lies in physics:

The wavelengths involved in these microwave cellular standards are in the range of 10 to 30 cm.

Efficient antennas are typically in the order of ¼ of the wavelength, but using very narrowband designs, or very high \$\varepsilon\$ chip antennas, you can maybe shrink them down to a couple of centimeters.

Below that, you simply can no longer efficiently capture (or emit) radio wave energy, and thus, can't communicate with the network. 

So, antennas set a natural lower boundary for what is possible, size-wise.

You could of course try to move the antenna off-board (which might be very wise, if you plan to mount things e.g. in a pipe), but vibration-safe RF connectors are way more complex, expensive, and possibly not even significantly smaller than antennas.