Pretty much all electricity will end up as heat somewhere down the line. How localized that heating is initially does not matter much.

Also all the energy consumption of data centers in the world (~500TW/h) is not enough to heat the planet a billionth' of a degree annually. It simply does not register.

Global warming is not driven by the energy we convert into heat, that's miniscule. It's driven by changes in Earth’s atmosphere (and surface) that limit how effectively the planet can reflect incoming sunlight and release heat into space.

https://youtu.be/_bP80DEAbuo?si=d8ZZCMVa9txyopRs