The suggestion made by YoustayIgo that a biologically immortal doesn't need to slow down makes considerable sense. The proposition that a galactic superpower with its "communication is limited by c and travel by fractions of c" also makes considerable sense.
It is worth looking at some of the queries forming part of your whole post to clarify the issues for a galactic superpower.
"What's a hundred year journey to a fifty thousand old person?" Well compared to human beings with a life expectancy of eighty years (it is true that many countries have populations with longer life expectancies, but this figure will serve as a benchmark). This is the of a 58.4 day journey one way for a human being. In this day and age, journeys with this duration are rare. Although some sea journeys will be this long. prior to the twentieth century such journeys and much longer were commonplace. So definitely your galactic aliens will have to deal with many such long journeys. These may not be insuperable, but they could be discomforting.
If the region they dominate covers several thousand light years either the aliens must travel extremely close to lightspeed to reduce their travel time with relativistic time dilation or use some form of biosuspension like cryogenic suspended animation. Other options include disassembling their bodies and then reconstituting themselves at their destination or even living through the entire journeys, presumably undertaking whatever work is required to maintain their galactic domain.
The main drawback to relativistic interstellar travel, of travelling close to lightspeed, is that it is extremely energy hungry. A sensible galactic superpower might be more inclined to travel more slowly, though this can still be at a reasonable fraction of lighspeed.
Currently human technology is not able to detect alien life on the exoplanets we know about to any degree of certainty. New missions in the near-future will start to change this. But we will still be far from being able to detect evidence of alien civilizations on any exoplanets.
If this galactic superpower maintains a large fleet of interstellar vehicles that are engaged in traversing across their domain of, at least, five thousand light years could this be detected?
Firstly, this depends on their means of propulsion. For example, fusion plasma propulsion systems could leave an exhaust trail. Again whether this is detectable depends on the scale and duration of the acceleration and deceleration phases of the spacecraft. For example, if the spacecraft accelerates to 0.1 c at 1 g the duration will be approximately five weeks. Ditto for its deceleration phase. So if we kept observing plasma jets either beginning or terminating at specific stars this would indicate the presence of fusion propulsion spaceships.
Of course, this could involve long observation periods. Basically we would need to be lucky to see, at least, one fusion starship during its active phase. Then we would need to look for more, spotting those again depends on how many vehicles leave or arrive at that star. If the rate was one per century, then it will be a long wait. While one per month might stand out as completely obvious.
Fusion propulsion has been used as an example. It is also that the galactic superpower's vessels use propulsion systems that don't have observable effects. For example, if they used an Alcubierre sublight drive, while this could have major local effects there might be nothing to be seen at a distance. In that case, billions of starships could be cruising through the domain of the galactic superpower and be unobserved.
What about their communications? Could these be observed? Probably, a galactic superpower will have learned to operate in an energy efficient and conservative manner. This will ensure their long-term survival. Communications will be by laser or maser channels aimed directly at the systems of their recipients. This means little in the way of side-channel signals that can be eavesdropped upon or observed.
Any navigation beacons won't blasting out high-powered signals, highly advanced technology will be capable of detecting even very weak or low-powered signals. They won't be broadcasting their presence to the rest of the galaxy.
In essence, even a galactic superpower spread across five thousand light years won't necessarily be sending out signs or signals that will clearly advertise its presence or its existence. Such a civilization will have learned how use its energy effectively and efficiently without leaking out any signals that show it is there.
Even against the vast scale of the galaxy and the niche in it that the galactic superpower occupies it will be extremely hard to detect them. It is little wonder the human species hasn't done so.