The streaking is ringing in the signal, usually caused by components in the analog circuitry wearing out (most commonly capacitors.) iMac G3s are hot boxes with no fan that tend to run smokin' hot, I'm honestly surprised they survived this long.
I would suggest recapping the entire unit and see if that sorts the issues out. If it doesn't, you're looking at some complicated analog signal debugging. I know the early iMac G3s with the tray loading optical drive had severe problems with bad capacitors, but the later slot loading models usually didn't. But the caps in those units are all now over a decade old, and have been run smokin' hot, so they're going to be worn out.
The cathode ray tube itself could never develop smearing/streaking as a failure mode, it's all caused by the electronics that drive it. Tubes themselves can experience only a few specific failures, like the guns wearing out and causing color problems, the heater going dark which makes the tube darker, shorts in the neck guns and outgassing.
