BTW those Thorn tubes are most likely from the early 1980's, the first generation of low power tubes. The original design calls for the full power tubes to be 40W, but in the first oil crisis and for residential use the power ratings were reduced to lower power but still compatible with the existing ballast equipment.
With the current trace, the beginning section is the glow discharge in the starter, then the HF is the arcing as the contacts close. Then you have the filament heating, showing the core saturating. Then the start attempts, the tube not being able to conduct and thus restriking the arc in the starter until the tube finally strikes, where you will see the high amount of third harmonic distortion in the current waveform. In the starter trace you see the low current that ionises the gas fill in it and heats it uo, the uneven current is due to the different areas of each contact acting as a very poor rectifier. Then the preheat phase and finally only the high frequency current flow that is through the small capacitor in the starter.
In the PFC capacitor there is a lot of distortion, it would look different if you placed the probe on the incoming mains waveform.
BTW there should be a higher light output from the new tubes, you have gone from a 26W tube to one with 37W input power, so there you have 30% more power to be converted to light. Why do you not just use the 2 tubes the fitting is designed to use, you need a good light output so why not use the correct number of tubes per fitting. Using one and moaning about poor light is not good.
The tubes all contain mercury, it works on a gas discharge in a low pressure neon/argon gas column to ionise the mercury to produce UV light which is converted to visible light in the phosphor. The NEC tubes are made in Japan, good tubes with hopefully a good life.
BTW do not buy the LED retrofit tubes, you will find that they are absolute shite, with half the lumen output when new, and degrade badly in the first year. They are only good in cold stores where ordinary flourescent lamps perform poorly because they are too cold.