Maybe hire a team of architects, engineers and machinists to build machines that automate the building of "earth ships" and subterranean farms, ranches, homes, stores, roads, water storage and treatment, sewage treatment, walking and biking tunnels, light bending and directing mirrors / lenses under ground in places that will become too hot to survive. Each living unit must be modular and expandable yet engineered to survive significant asteroid impacts and last millions of years.

With time some of the tunnels would extend out below the oceans to further increase the probability that humans could survive a blanket of large asteroids and comets with the side effect of negating the usefulness of nuclear weapons thus nuclear weapons could be dismantled and repurposed in mini-micro-mini-micro subterranean nuclear power stations interlinked into neighborhood meshes. Every neighborhood would have a few dozen coolant filled clay heat batteries that would bring every home, road and walkway to 65F (18C) with fresh filtered air from the surface and from air storage geothermal tunnels.

With time the equipment and automation would sufficiently advance to move faster and more efficient. One trillion dollars will not be enough to complete the jobs, but rather to make an optimized blueprint so that every country can repeat and improve upon the process until the entire surface of the planet could be used to produce food until such a time that it has to be produced under ground. Anyone passing by the Earth should be convinced that the entire civilization is agrarian and non-technical thus not a threat. If the tunnels are deep enough and the tunnels are shielded enough from space then fiber networks could share a backup GPS network to reduce dependency on low powered space transmitters.

I believe this would be much easier to accomplish than moving parts of our civilization to the moon and especially more practical and safer than Mars.

50% would go to scholarships / apprenticeships for young and talented scientists and artists.

25% to foundational longevity research.

25% for cultural preservation projects in Europe.

Fund medical research for things that have no profit motive for pharmaceutical companies, such as rare diseases, psychedelics, herbal remedies or off-patent medications.

Long term funding for the Linux desktop, especially those areas that don't lend themselves very well to the bazaar model.

Depends. A trillion dollars in cash is different to a trillion in stock.

If if was in cash, the money will go back into donations, charities, invest it in more startups ad the majority to fund for research.

Probably I would buy some lichi, because I always wanted to taste it, but costs an arm and leg where I live. Not sure what I'd do with the change.

Fix global society so it can fix the climate catastrophe. Start by educating everyone so they can read and think at a post highschool level.