Yes, banks should worry about all these risks. Climate change is a large systematic risk so it make sense to worry about it as well.
Meanwhile, megabanks like Wells Fargo are backsliding on their previous climate pledges and exiting from the Net-Zero Banking Alliance, a United Nations-backed group that encouraged members to slash their emissions in line with the Paris Agreement.
Multiple US banks and entities are backtracking their goals of lowering emissions, wich is the main solution to limit the risks of climate change.
They're setting themselves up, and us collectively, for higher risks of flood, drought, sea rise, ...
Sustainability is not typically part of a bank's vocabulary.
But there are terms a bank can understand : systemic risk for the economy, the prospect of fossil fuel investments becoming stranded assets, negative effect on public relation and how it can be a competitive disadvantage if a bank do not attract customers who value human life.