Fermi and pals (and people before, and after) were postulating two things, one of which is related to the EM observeability, hence the Drake equation and so on.
There's another aspect other than EM and that's any other evidence, like say stellar body-level engineering. Things very big and easy to see, that don't look natural. Every time something weird is seen in the heavens, that's always in the back of astronomer's minds.
Their other point was that the assumption that advanced civilizations were space-farers, and that given the millions of years of timescale, the milky way ought to have been well traversed by aliens. So that means they might have come past - not recently perhaps - but they might have left something that is visible.
It's a favorite topic in SF land, and every author or would-be author has their pet theories as to what are the major factors in the lack of observe-ability. One popular one is that there are Bad Things out there. If you get seen, you get killed, so those smart enough to work it out go quiet. It's nonsense that depends on EM visibility, and Bad Things being able to suddenly turn up and make things hard for you, but hey, it makes good SF books.
A more realistic one is that civilizations that arise out of a competitive evolutionary strategy (like all life on Earth) and probably quite prone to self-destruction. So basically civilization duration towards the shorter end of the scale.
Secondly, spare faring is dumb. Gravity wells are are deep, and it costs about 30kg of propellant to get 1kg in orbit. Sure.... it could get better, nuclear rockets maybe, space elevators, but by the time you're there, you care less about such childish things. Instead of sizing up like our primitive monkey brains tend to conceive, one can also size down. I think we even see that on Earth.
So worst case, we go up in a mushroom cloud, best case we'll all just say fuck it and upload ourselves to a never ending series of better-than-life videogames. Either way, not much to see. It's probably a good thing. If other civilizations end up like ours, I'm not sure the universe wants them hanging around forever.