You might, the rest of us not so much.
I think it would take many orders of magnitude more than plenty. Any kind of generational plan will depend on future descendants being willing and motivated to continue dumping vast amounts of time, resources and human lives into a project that won’t come close to benefiting the original designers.
That’s not taking into account that there will have to be some powerful motivations for the PTB to direct that kind funding towards a project like that.
My personal opinion is that the solution to the Fermi Paradox will come down to mundane things. Space is too big, intelligent species don’t last long enough, governments won’t fund things, etc.
Of course, you and I will never know but I don’t think humans will ever build Dyson Spheres of self replicating probes. Those things are just not practically possible.
We shouldn’t look at Dyson Swarms as some kind of giant organized project mankind or other species undertakes. Much more likely it will emerge from thr energy needs of a society over a very long time.
Imagine that you use up the energy available on Earth. Long before you get to that point, energy will become so expensive that we will ring the earth with solar power satellites until there is no more light to capture or until we’ve blocked too much sunlight to be healthy… Energy gets even more expensive at that point, so we start moving manufacturing out of Earth orbit where there is still lots of energy to be had. So we do the same thing on other planets where we can, and ring them with solar collectors as well.
Eventually, you’ve used all the energy available on the surface of the planets and moons, so you start building energy collecting facilities in solar orbit. Eventually you wind up,with a ‘Dyson swarm’ blocking a significant amount of light from a star. It could happen a little bit at a time, over millions of years.
We think of Dyson Spheres as something that blocks almost all the light from a star, because a solid sphere would. What we should really be talking about is ‘Dyson dimming’ as a continuum. ET could put up Dyson swarms that block anything from an infinitesimal amount of starlight to ones that block a significant percentage. technically, any civilization building solar powered probes in solar orbit (including us today) has a 'Dyson swarm ’ in the sense that we’ve built artificial objects that partially block starlight when they occlude the star from someone else’s perspective.
From there it’s just a matter of degree. Maybe it takes so long and so much material and energy to actually block most of a star’s light that the universe is littered with dead civilizations at varying stages of completeness of their own Dyson swarms, woth most never getting to the point where they block more than a few percent of a star’s light and are almost undetectable by us.
One other factor is that practical limits and required spacing between swarm satellites might put an upper bound on how much starlight can be captured. A dyson swarm might have a very low ‘fill factor’ due to required spacing between satellites. Maybe the best you can do is to capture only a few percent of a star’s light and most Dyson swarms out there only collect a fraction of a percent.
These are some examples of the ‘unknowns’ that rarely get talked about but could be critical to understanding what we do or don’t see.
What is the end game of acquiring any knowledge at all?
Take the most famous problem in my field Is P = NP?
If the answer is “No” then very little changes. Nothing changes at all for the person on the street.
You might think that this makes certain cryptosystems provably hard. Nope. Just because a problem is provably hard in general doesn’t make it hard in all cases. And telling which cases are the hard ones is a whole 'nuther problem.
Which leads to the other side, whether P = NP or not, people have worked and will continue to work to find broad cases of NP-hard problems that can be solved efficiently. That won’t change.
And if P = NP is true, the end game might not be all that world changing. The exponents of the poly time might be unrealistically high, other impracticalities might occur, etc.
As the plaque on the statue of Emil Ferber says: “Knowledge is good.”
Note that especially in Math, you just don’t know whether or not a result will ever lead to anything practical. Mathematician G. H. Hardy loved Pure Math since
“I have never done anything “useful”. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”
Well, us CS folk came along a found a ton of uses for it well after he died.
Note that one of Sen Proxmire’s notorious Golden Fleece awards went to SETI. A decision he later repented.
(And of course there’s the alleged remark by Ben Franklin on a short demonstration balloon flight: “What good is a newborn baby?”)
More directly answering the question about SETI’s ‘end game’, in terms of searching we are seeing a shift away from radio SETI and towards ‘artifact SETI’, such as looking for technosignatures and alien artifacts.
One of the potential answers to the Fermi paradox is that civilizations don’t last very long, and therefore it’s simply rare for civilizations to overlap each other. We’re alone, but so were a million other civilizations before us. If that’s the case, we’ll never hear from another civilization but the universe is littered with the remnants of dead ones.
Let’s go a little further. Let’s assume that Earthlike planets with life are rare, and that many technological species had the ability to detect Earth and life on it. If that’s the case, we may have been visited in the past. Maybe many times, by many species all long dead. But in geologic time, the Earth resurfaces itself and any evidence of them on Earth say, two billion years ago would be comoletely lost.
But if you wanted to observe the Earth for a long time, where would you put your observation station? Hey, luckily that planet with life also has a big, airless moon that’s tidally locked. A station on the near side could observe the Earth continuously. If you were an alien civilization that wanted to check on the Earth over millions of years, that would be where you’d put your stuff.
So ironically, the best way to find aliens might be to look on our own Moon. Look in protected spaces with a view of Earth where meteorites aren’t a large risk. A skylight in a lava tube with a view of Earth would also be protected from cosmic radiattion, temperature swings, and being spotted from Earth. I actually have science fiction outline for a story of that sort. The first explorers in a lava tube skylight descend into it and find it packed with alien machinery.
I’m more curious about what we do if it continues to fail. 
What responsibilities to life in a dead universe are impose on us and do we have to do anything about it?
From what I’ve read about Dyson Spheres/Swarms, it would require a giant organized project. I read a paper where it calculated the mass required to put enough solar collectors around the sun would entail planet mining. But maybe, as you say, if done incrementally, it would be more practical.
There’s also the problem of collecting the suns rays, converting to energy and beaming it down to earth. There is a lot of loss in that system.
In regards to the Fermi Paradox, all of that spent energy in the form of heat will need piped away from earth leaving a thermal signature.
That’s why I think looking for star dimming is not a good way to look for aliens. I don’t think Dyson Swarms will be their give away.
This is what I believe.
Speaking of Artifact SETI:
Avi Loeb, an astronomer at Harvard famous for claiming that Oumouamoua was possibly an alien spaceship, had a pretty good idea: Pour through the records of meteors, looking for ones with speeds that meant they were interstellar, then look for debris.
They found a meteor that fit the bill, one which crashed off the coast of Australia. Loeb mounted an expedition to the area and started dragging it with magnetic sleds. They just announced that theynhave found fragments of advanced steel alloys in their search.
It’s almost certainly not aliens, but there’s an actual falsifiable test: Steel made on Earth has trace elements that have fairly short half lives. But if this is an alien material, it would have been made millions of years ago and would have none of those shorter-lived elements in it.
My money is on the material being left over from WWII: exploded bomb casing, fragments of a detonated mine, falling metal from aerial combat or flak, etc. It rained metal for many years in the Pacific.
We’ll have to wait for the material testing to know for sure.