At first, there was joy; then came the confusion, which led to anger, eventually subsumed by fear. Finally, control was established, resulting in glorious victory, and giving birth to new hope!
In other words, I think I've gotten a handle on how this update works. Sort of.
So, supplies are crazy expensive. How to not waste them:
Watch your logistics rating, anything below 100% will cost extra supplies.
Bring freighters, it's terrible to get critically needed supplies only to watch them hemorrhage out rapidly due to your suddenly 10% logistics.
Don't repair prizes, they will cost more in supplies than you will receive in credits.
Mothball ships you aren't using, they cost essentially nothing both in terms of supplies and logistics.
Minimize the number of ships replenishing CR, ships with full CR use a fraction of the supplies.
Consider your deployments. It's not worth chasing down fighters and frigates if you already have destroyers to loot.
Don't use too many interceptors. Talons use 4 supplies/day, Wasps use 9, a Hyperion uses 3.
Minimize/forego the use of marines, each 10 marines cost 1 supply per day. I finally got my (large) fleet's supply usage down to 45/day, 30 of which is my 300 marines.