I'm afraid that all 'faster-than-light' technologies are quite literally 'wishful thinking', in that we have used our great monkey brains to imagine what we want and created imaginary technologies to flesh out those fantasies. The truth is, the entire universe is set up so that nothing can travel faster than light. Those are the rules.
But let's imagine for a moment that faster-than-light travel and communication are possible (There is no practical difference between these two concepts; if you could send information, you could send enough data to build a sentient being, or an army of them). If the alien civilisations of our galaxy have faster-than-light capabilities (hint- they don't) then suddenly the Fermi Paradox gets a lot more problematic. Whereas before we only had to worry about explaining why no-one had arrived from nearby stars, within a few tens of light years (at speeds that would require journeys of decades at least), now we have to explain why the civilisations a hundred light years away can't get here, or a thousand light years away, or a million. If we accept that ultralight travel is possible, we have to account for the absence of spacecraft from the entire visible universe, not to mention the ones outside the Hubble Volume.
Worse than that, the concept of faster-than-light travel brings with it a much worse problem- time travel. Any method of faster-than-light travel enables the reversal of causality, so that messages (and even physical objects, such as spacecraft) can be transferred back into the past light-cones of any given observer. That would enable - no, require - any civilisation capable of travelling faster than light to go back into their own past and change events for good or bad. The whole universe would become a vast demonstration of the Butterfly Effect, where a little change in the past causes chaotic changes in the present.
And finally, most people get the central question of the Fermi Paradox wrong; it isn't 'Why can't we see them?' it is 'Why aren't they here?' Given faster-than-light travel and reversable causality, all the advanced alien civilisations for millions of light years around should have been here long ago. We would have been colonised, or conquered, as far back as the Precambrian. We would have been learning about the Great Galactic civilisiation in our schools for millions of years.
We haven't, and that suggests very strongly that FLT cannot happen.