Honestly, I've rarely seen such cohesion loss after a 1 turn journey on transports.
Some things I've noticed:
Every ocean and coastal region the fleet sailed through (looking at the move plot from the previous turn before your force arrived in NOLA) was "rain" including the Lower Mississippi River in front of NOLA, although on land on both sides of the river the weather is clear
. Poor weather means cohesion loss.
The last Movement message (29/29) says that Farragut's fleet "suffered 22 hit(s) from foul weather and/or exhaustion".
Battle messages says "Fort Jackson bombarded us and our D. Farragut's Fleet took 43 hits. We returned fire, dealing 8 hits to them.". Taking bombardment causes cohesion loss to the targets, even transported troops.
Your force then debarked into NOLA, which itself will cause cohesion loss.
The NOLA battle report doesn't show what cohesion your forces had before or after the battle, so that doesn't help much, but just being in battle, even elements which did not directly fight, can cause a net cohesion loss for involved troops.
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Other things of note not directly related to cohesion loss:
Your invasion forces doesn't have a single supply unit, which is sub-optimal for drawing supplies from Farragut's fleet.
Put 1 or two of your divisions into PP so that they recover as quickly as possible, leaving the other 2 or three in DP to besiege NOLA and defend against attack from elsewhere.
I actually only ever invade NOLA at Fort Pike, take it quickly to have a supply base and then march on NOLA, one region to the west. I don't like running the forts nor attacking them first. I guess I'm just a conservative attacker.
Good luck.