One thing to remember about silica gel. It has a limited capacity to adsorb moisture.
I suspect that the combination of a "less than perfect" sealing of the sphere and age, results in the silica packs becoming saturated.
They can be reactivated by heating - although the plastic bag containing the adsorbent might not be heat safe without vacuum.
Ideally, you heat these under vacuum - the moisture comes off at a lower temperature.
Or, just replace the package and use some silicone grease to improve the seal.
The pictures of the disassembled globe are invaluable! Thanks for sharing this.
Replacement silica gel packages should be available from most online technology sellers.