Does a cartridge that has been in storage for an extended period need play time…

Some other advice not related to your question: the input impedance of your phono stage should ideally be 10X or more greater than the cartridge’s internal impedance.

Atmasphere, Your experience runs counter to mine. One can never know if a cartridge we like in the present might have sounded even better when it was fresh out of manufacture, so I certainly would not claim that suspensions do not degrade over time. But nearly all but one or two of my cartridges is at least 5 years old, typically more like 20-30 years old, and only once have I found that the sound quality seriously degraded over time. This was for a Grado TLZ that I purchased new back in the 80s and used to like quite a bit. It was my only cartridge for a few years back then. These days it no longer sounds even "good"; I don’t use it. Otherwise, I’ve had no issues that I can knowingly ascribe to suspension degradation, given the point I made above, that we can’t know how any "old" cartridge sounded when truly new.

I regularly wake up my cartridges by playing bands 2a,b, and c, of the original Cardas test LP. (The latest version does this at 45 rpm on side 1.) if that doesn’t help, you may have a problem with suspension. On the other hand, I own many 30+ year old cartridges and all but one have had no problem.