Then difference would be observed between superimposed and semiparallel eectronic ignitors as well, the latter use the ballast as the pulse generator, thats some big energy stored in that core compared to the tiny superimposed pulse transformer....

I Dont have any data to tell the actual effect, gotta do tests to see difference...

Deleted

Its not the sort of thing you can easily see, especially s arc tube end blacening is normal for HPS, and as most damage is from the time of warm up after ignition and not from ignition itself

@imj: Are you sure it was a lumen depression and not only the condensed mercury/sodium (quickly evaporated by the sudden current)? With many lamps I observed quite dense foggy cloud formed on the arctube around electrodes, but after full warmup it always disappeared. And the same for some fluorescents - after startup a gray cloud appeared on the tube around the electrodes, but after warmup it slowly disappeared (fluorescents take way longer time to evaporate this cloud, but they do so; it usually start to clean up from the place closest to the filament, so in fact the place, what heat up the quickest)...

And for the electronic "instant start": I haven't understand from your text, if you observed the instant start to make denser, or lighter cloud than the preheat?
Many of these do heat up the electrodes by quite large power, so even when the lamp start quickly, the filament is frequently quite heated a lot at the time of ignition, so the real wear is not as large. But this quick warmup frequently make the mercury, which condensed on the filament, evaporate in nearly an explosion, so it then tend to land and condense on the cooler glass nearby.
But those simplest ballasts tend to vary a lot between individual pieces (some ignite the lamp really with cold electrodes, some have lower voltage and so heat them up first), but even when they ignite the arc on cold electrodes, they still provide huge heating power till the discharge turn into a low cathode drop arc, so the glow phase last quite short time...

And what about the wear from the "exploding mercury" eg the mercury pushing off particles of the emitter as well ?

It sits on naked parts of the filament - so on places, where the coat was already consumed, or was never present. Therefore the new lamps do not have this effect as pronounced as older lamps do.

In any case, none of these quick formed gray cloud lasted longer than few hours of burning.
The persistent cloud made of really sputtered electrode have a bit different shade, but mainly it build up only very slowly, so you never notice it on a lamp you see daily (you get used to it's appearance, so you never notice anything suspicious).
And mainly the dark sputter start to form only after significant part of the active emission layer is either consumed (on old lamps), or contaminated (so the discharge root prefer the naked metal)

Deleted

The different ballast concepts do behave differently in the formation of the mercury condensation.

But it is my observation as well, than  the simplest electronic inverters of the European style (so with filament in the resonant circuits) very frequently do wear the lamps less than the glowbottle starters on a preheat ballast.
The white glow during the preheat mean there is a thermionic discharge, but it does not automatically mean the filament has warmed up enough to handle the ballast current. For the thermionic discharge it is enough only the filament ends get warmed up, but for the lamp operation the central section is of way more importance and it take really the full specified heating time (~2.5sec on a lamp rated current, 1 second on 2x the rated current, 0.5 second on 3x the current rating; on higher current the thermionic discharge start way before the filaments are actually heated up correctly) for even the central section to heat up properly. The presence of the discharge across the filament is more steered by the voltage drop across the filament (peaks above 10V) and not as much the temperature of the bulk of the filament. And don't forget, than the naked parts of the filament heat up way quicker and to higher temperatures (so become sufficient for the thermionic discharge) than the part covered by the emission coat, but the current capability of those hot ends is way insufficient top carry the main discharge current.

Well, both preheat and the simple electronic ignite the lamp with not yet sufficient cathode temperature. The discharge start as a glow discharge and only then the cathode warm up fully. What play a role here is the time, how long the discharge spend in the glow mode. The preheat circuit continue to warm up the electrodes only by the cathode fall and the discharge current, what take time. The resonant circuit of the electronic supply quite a lot of current (because of the larger drop across the tube), what really heat up the electrodes very fast, so limit the time the cathodes are exposed to the damaging glow discharge.

For proper heatup during the preheat you really need the 2 seconds preheat time on a standard choke ballast, even when the thermionic discharge appear just after half a second.