@jawlessphoenix
Currency for storage upgrade (coins) is not effected by the storage limit
Do shifts, forfeit the resources (police: donuts, flashlights, etc. movie: popcorn, coffee etc, Hospital: bandages, charts etc) you need to unlock/upgrade rooms and just collect the coins to be able to afford a storage upgrade
You can also trade resources to make a little more room, go to the workplace: top left, workplace icon: choose the tab with two arrows to trade
Ex 10 flashlights + 10 Walkie talkies will give you 5 donuts, it will free up 15 slots
Not much but better than nothing
I know it feels like a waste of resources, forfeiting things and just getting the coins, but what else can you do?
If you have enough sims, choose 2 that are not specialized to do shifts and collect coins, that will be faster
Prioritize upgrading your storage, instead of trading coins for resources, until you think you have enough storage to hold what it takes to unlock the last rooms (for the police I have a storage of 4000 and have not yet unlocked the upstairs rooms)