Is this “heat leaking” really a problem?

Not yet. We'd need another century or two of energy consumption growth before it becomes really significant. The CO~2~ thing is actually very specific to our current way of generating power and avoidable - they conflated it a bit in the headline, probably for clicks.

Fundamentally, economic growth on Earth (probably, barring new physics) can't continue forever. It's a finite lump of matter, there's finite ways of arranging it, and one or more arrangements will be the best while still respecting things like thermodynamics. Once we get there, there's nothing to improve.