Presumably Starlink for routing throughout space. Google does under-sea cables and domestic internet access too.

They invested in SpaceX long before Starlink was a thibgy

Starlink wasn't working yet, but had been announced as a thing they intended to do.

Ehh, more like Starlink was a thing they said they'd do to justify the investment at the time. Just like they said they'd build an assembly line mass producing Falcon 1's for small launch market, or send a Starship full of artists around the Moon. The first prototypes were three years later.

Having your exponentially more expensive fleet of satellites constantly burning up versus dedicated cables that rarely need replacing

The big use-case for Starlink is typically for people in locations without dedicated cables.

All energy generated on earth contributes to global warming, even solar panels which decrease Earth's albedo. If you care about climate change and the earth you should want the datacenters to be in space.

The earth is limited in the amount of thermal energy it can radiate.

Ah yes, burn thousands of tonnes of methane (assuming Spacex) to launch a data centre satellite into an orbit, then burn thousands more to maintain it and update compute or burn the entire thing in the upper atmosphere, to avoid contributing to global warming by not burning all of that fuel and dry mass.

Uh, that's not how global warming works, you know.