Welcome to the instance! I'm very glad you brought this over here! I'm really hoping to run some of these ideas past folks who know more than I do! I'm thinking about doing some art if I can be sure the details are correct enough.
There's some redundancy with your summary but I thought I'd copy my comment over just in case:
"I really like figuring out scenes/aspects of solarpunk that don't normally make it into the visual art, so I'm glad you're thinking about this and starting a discussion!
Some cities are going all in on 'sponge city' water management techniques, but as far as I know, they're above sea level, often with depleted aquifers under them waiting to be refilled. I have no idea if any of those practices are applicable in New Orleans.
It may be that some areas just aren't practical locations for permanent human settlements, or that they become less-so with worsening weather, and that may be something people will need to make decisions on in the future - at what point is rebuilding just throwing good resources after bad? But there's a tremendous amount of history and culture in these places that absolutely should be preserved, so I'd love to see city designs that can accomplish that.
I've never been to New Orleans but I've seen those stilt houses in other areas in the American south and I think the designs are really cool (concrete reliance aside, but geopolymers may offer an alternative there?). They at least show a recognition that this space is routinely underwater and a willingness to adapt which I think fits a solarpunk ethos.
Rebuilding city structures in a similar way, on stilts or with open bottom floors, could provide some really cool opportunities for common spaces/third places whenever they're dry. Depending on how high the buildings need to be, you could have a decent amount of headroom, room enough for parks, playgrounds, skate parks, parkour courses, anything that can be submerged and washed clean or stowed in the preparations for a storm. It might sound like they'd be dark and grungy but I think they could be really nice, sheltered from overhead sun, with room for a breeze to blow through.
For buildings of extreme historical value, it might be possible to lift some onto raised platforms preemptively rather than wait for rebuilding. I know people move important buildings sometimes so that seems within the scope of human accomplishment.
(Though I'm from a place where our ground is very stable and features a lot of ledge - I have no idea what the ground is like in your area or what it takes to build structures that won't shift, especially once partially submerged (and the ground thoroughly soaked). These ideas might make for cool art/fiction but be completely impractical, I assume folks down there have been thinking about these problems for much longer than I have.)
Another solarpunk option might be accepting a certain amount of encroachment by the water, and switching to canals, ropeways, raised walkways, etc for getting around. This probably still assumes buildings will raised, which still requires a fair amount of changes to the area.
I'm looking forward to seeing what everyone else comes up with.
Edit to add my SO's suggestion: city of houseboats/rafts/riverboats. Or maybe a mix of that, the encroachment/canals, and the raised buildings?"
Now that I've been thinking more on it, I have a few more thoughts:
Solar daylighting rigs (the fiberoptic type) could really help with the quality of the under-building spaces. That could be nice for sports areas, market places, etc.
If the sewage system descends from the building and slopes back towards higher ground or wherever they put the water treatment site, it could end up overhead for those low spaces, so we might want a double layer system or something? Composting (maybe even localized anerobic composting/biogas generation?) would be another option I suppose.
I brought this question up on the Fully Automated TTRPG discord and cromlygames suggested a public transit fleet which is built to be amphibious so it can help with mass evacuations in worst case scenarios. His design ideas was "Basically those ducktour buses (former America in Vietnam war amphibious APC), scaled up to London double decker bus. Door height set to match platform height for tram platforms. Assumes roads not blocked with debris or abandoned cars." He assures me the double decker bus design is surprisingly bottom-heavy and tip proof though I think some stabilizing pontoons that swing down might be neat.