What's a megaproject you know is probably a bad idea, but would be sorely tempted to try if you were the leader of a wealthy country?

make roko's basilisk and a time machine for the express purpose of bullying techbros for eternity.

After that? figure out how centralized of a metropolitan city can be made to make the smallest footprint yet densest population possible to see how that society would change when placed in such an environment.

Maybe figure out how to create seed space ships filled with bacteria'n'shit or whatever to possibly jump-start life on foreign planets, make them as resilient or whatever as possible to survive for immeasurable periods of time and attempt to seed life on all possible life-bearing planets. Definitely never will see any results from it and nobody will definitely will know if it's successful or not, but it seems like a neat thing to do.

maybe make a human machine immortality project that makes a gestalt entity out of all the people that hook up to it and let their noggins get uploaded to it before croaking and see if we can make a single super-entity that transcends the mortal form and possibly creating a new step in the evolution of humanity.