This math is wrong.
Back of the envelope: accelerating 250 x 10^6 kg to 1% of c over one year is about 310,000 TWh. That’s like half of current annual energy production.
Even at like 10g, which would accelerate that mass to 1% c in less than half a day, you’d only use like a tenth of our 10^22 joules of fossil fuel reserves.
> double that to slow down
Why the asymmetry? 1x to accelerate, 1x to decelerate. (Less if you can aerobrake and/or use gravity assists.)
Taking the 310k TWh from earlier and doubling it, and assuming 18 MeV for D-T direct-drive fusion, and you need 6,600 kg fuel for the journey. (Plus propellant.) 100x that to account for inefficiency and cooling and you have 660 metric tonnes of hydrogen. That, if kept in its bastard liquid form, takes up about 3 Olympic-size swimming pools in volume.
Shame we don't have a way to efficiently convert fuel energy directly into a ship's kinetic energy, and have to go via conservation of momentum… though I suppose magnetic launch of interstellar vehicles would be a neat use for a Dyson shell or Niven ring?: https://www.wolframalpha.com/input?i=0.5+*+1+gee+*+%280.01c%...
https://projectrho.com/public_html/rocket/
It's _full_ of good stuff.
Still, even half of current annual production is quite a ask. For single ship, and I might venture to guess that 250e6 kg might be light for what is needed...
Then double that to slow down. And remember efficiency and that well you need to spend some to keep people alive...
Seems like energy in general is one of the true problems.