Musk spends half his time on electric cars, solar power, and grid storage, plus he just donated $100M for a carbon capture XPrize. He's probably had more positive impact on climate change than any other human on the planet. I doubt other car companies would be so far along on electric cars if Tesla hadn't forced the issue.
Bezos hasn't been that focused on climate but in 2020 he did donate $10 billion to his Earth Fund.
He also pledged to make Amazon a carbon neutral company by 2040, which combined with the implicit goal of Amazon taking over the entire world economy (joking not joking) is a big deal.
"The environmental problems we have can't be solved by a couple of billionaires."
Plenty of relatively poor people have devoted their entire lives to working to help the environment, despite knowing their impact will be much smaller than what even a mere millionaire could accomplish.
Billionaires don't need to fix all environmental problems to make a very significant difference.
And what if we cannot acheive it, because of political and economical system at play i.e. local maxima holding us back and prevents us from breaking away from current order of things?
Going to another planet will not help with that. Pretty much no matter what happens on Earth, it will still be orders of magnitude easier to live here than in another planet.