I have been unable to find pint jars for months, so I bought a few Rubbermaid Brilliance containers to store new tobacco in. They have a full rubber seal around the lids, and come in a lot of different sizes. Downside is they are waaaaaaaaaaaaay more expensive than jars! But they seem to work perfectly fine, and once jars are available, should work great for storing leftovers in the fridge...
I recently discovered several tins of tobacco in storage that I bought back in the early 2000's. The tins were opened, covered with their plastic lids, but stored where temperature and humidity were not controlled for 10–15 years. I tried to rehumidify one tin, but things did not go so well. The other tins, despite being quite dry, smoked just like they did a decade or more ago. I'm sure there are benefits to storing in better containers and conditions for long term cellaring, but there is no need to get crazy trying to do anything special short term.