CB is HF and much, much, much less affected by atmospheric moisture than UHF.
The tube at the bottom of your antenna that surrounds the connection should have provided a measure of protection.
PL-259 connectors are not waterproof so rain can get into your coax cable dielectric. Once it does, the only thing you can do is cut off the end of the cable to get rid of the portion of cable that moisture has infiltrated. The cables used “in the CB days” were a completely different type and perhaps didn’t allow moisture to enter the dielectric or the lower frequencies weren’t affected as much by moisture.
The radials on your antenna serve as the ground plane. Having the mast grounded should have no effect on RF, but is helpful to reduce interference and protect against static electricity.