Hello; This may add to the confusion but also may help. The upfront question is what you intend to do with the sponge filter.
Use #1 is to use it like a brand new sponge filter. That being that it provides aeration by the air bubbles, helps create some mild water flow, breaks the water surface and some very limited mechanical filtration (The sponge will become loaded with fine stuff over time).
Use #2 is to act a seeding source for beneficial bacteria (bb) which will help get a new tank up and running and shorten the "cycle" every tank needs to be established and healthy for the fish. That you stated it will be a while before you start up a tank,
be a while before I'll have my tank setup to be able to put water In it
then the old sponge may not have the bb available later on in time. The bb are alive and the point of using a sponge filter to seed a new tank is that they need to be used fairly quickly. You can keep the bb going by some methods but I will not go into this. My take being that you will not be using the sponge filter as a seed source due to the time delay.
That said, my take is that the sponge will be Use #1. That being the case you do not have to do much of anything with it. I have several old sponge filters on hand.
Some were taken from a tank and thrown into a container just the way they were and left that way to dry up. When I need them I clean them up.
Others have been rinsed well when first removed the old tank and then placed into storage. This is the better method as it is easier to clean out the fine stuff while still wet. Just stick it in clean water and squeeze it a bunch until most of the stuff is out. I then allow them to dry out. It may be best to treat such stored equipment in a mild bleach solution prior to use in a new tank setup. If they are soaked in a bleach solution, this will kill off any bad bacteria and parasites and also the good bb and sort of place the sponge back like a new filter. If soaked in bleach you will need to treat them with a water conditioner product such as Prime or Safe to neutralize the Clorox.