Also, 25% of lightspeed is fairly aggressive. Even 1% would require engineering and energy reserves way beyond anything we can realistically hope for, largely due to the tyranny of the relativistic rocket equation[1]. Note that if you want to stop, you have to carry your own fuel, which makes the problem quadratically worse. Proposals like Breakthrough Starshot[3] can hope for 10% largely because they will just do a flyby and don't have to carry fuel for braking at the destination. Similar projects[4] have used much more realistic velocities and discovered in doesn't really matter - it still takes less than 100 million years to completely colonize every star in the galaxy.
But this model doesn't solve or address the Fermi Paradox - where is everybody? It actually makes it worse. We might overlook or not be able to see a single populated solar system halfway across the galaxy, but a civilization that has expanded to fill every nook and cranny of the galaxy should be fairly easy to spot, no? Obvious, even. Yet there is no sign - not in our solar system, not in radio signals, not in Dyson spheres, nothing. On the other hand, every time we still down and make reasonable assumptions about how long it would take a species to colonize the galaxy, we usually find that it should have happened hundreds of times over, billions of years ago. So where is everybody?
[1]: https://wmap.gsfc.nasa.gov/universe/uni_life.html
[2]: https://www.physlink.com/education/askexperts/ae465.cfm
[3]: https://en.wikipedia.org/wiki/Breakthrough_Starshot
[4]: https://www.extremetech.com/extreme/294051-scientists-simula...