I would imagine dyke schemes will be a solution for the mega metropolises. It's the poorer ones that will disappear.

I don't know the extent to which that's true. If even one of the many big and worsening storms causes enough damage to breach on a single occasion then the whole city floods to whatever level it would have otherwise and your efforts are for nothing.

There was a huge flood in the Netherlands in 1953 which killed thousands and as a result a big barricade of walls was built around the whole area. https://en.wikipedia.org/wiki/Delta_Works . There's been not even the slightest chance of flooding in that area since. Smart things with segmentation can also be done.

I think it is possible to hold this off for the richest cities. It'll cost a lot to build, maintain and perhaps even upgrade it, for sure. The Netherlands had the big benefit of a major natural gas find in that time that gave a huge boost to the economy, otherwise this wouldn't have been possible. Also, there were less environmental restrictions back then. All that will make it more expensive today.

On the other hand, the levee broke during Katrina in a first world country. Infrastructure needs to be improved and maintained continually and that's a huge problem and cost sink even in first world countries. Have you seen the price to build a mile of subway in NYC? The engineering marvel that will be required to save Manhattan will inevitably be the most costly thing ever built in the US.

New York will figure out how to save itself. It's all the poor towns and cities around the world that will be obvious problems.