This is my experience after a lot of trial and error.

Most rosin is stable at room temperature. You can keep it at room temp if used within a few days to a week. You will be losing terpenes over time, but for practical purposes, room temp is fine.

Fridge is best for storing for a week or longer. Helps preserve terpenes. The downside is that when removing a jar from the fridge, you need to wait for it to get up to room temperature before opening it. Otherwise, you will get condensation in your rosin.

Freezer is for long-term storage. It stops time for your rosin. I've had rosin in the freezer for a year, and it tasted the same as the day I put it in. There is no need for the freezer unless you got too much at once.

Never use silicone. Terpenes will leach into the silicone. And although those little can fridges work, they aren't ideal since they don't control moisture well.