While doing my research on HID ballasts, I have been seeing that many manufacturers give a +/- 10% voltage tolerance for CWA ballasts and a +/- 5-6% voltage tolerance for HX and reactor ballasts. I wonder how CWA ballasts are able to tolerate voltage spikes and voltage dips much better than HX and reactor ballasts and how CWA ballasts are better able to maintain lamp current over variations in mains voltage compared to HX and reactor ballasts.

The HX ballast uses the series LC tuned above the mains frequency to regulate the current. The capacitor you see there, the inductance is the leakage inductance between the primary and secondary made by jamming a magnetic shunt between the windings.
Now series LC alone still won't provide the current regulation yet,
but what it does is the overall reactance being the inductive reactance subtracted from the capacitive part.
This subtraction means if the inductive reactance gets reduced, less get subtracted, so the overall ballasting impedance increases.
That would still not form the extra regulation.
But what does that is, if you use a partially saturated core controlling that inductance.
Partially saturated means if the current gets higher for some reason (e.g. the mains voltage increases, so does the voltage drop across the LC combination), the inductance is driven deeper into saturation, so the inductance decreases. And that means less inductive reactance being subtracted, so the overall ballasting reactance becoming higher, countering the current increase in the first place.
This ability to counter the current change means the voltage needs to depart way more till the current reaches its tolerance limit for the particular lamp.
And hence the CWA offering wider tolerance of the operating mains voltage.

With the CWA the inductive component is the leakage inductance between primary and secondary, dictated by the magnetic shunt, aka a small stack of the transformer plate sheets put between the windings. And it is the saturation of this magnetic shunt (namely its ends), which then forms the partially saturated inductance behavior. Technically the same behavior ballast could be build in a series reactor format by placing series C and saturable L at 230V mains, but there it would need extra inductor to compensate the power factor. And that would mean extra cost and losses, so lighting system designs better ensure the tighter voltage tolerance (by sufficiently sizing the wires and more careful voltage setting on the distribution transformer), so it did not became such a thing as the CWA in the 120V world.
With CWA such inductor is made for free by leaving a small air gap in the core under the primary winding, so once the two windings are necessary to provide the voltage transformer function, the power factor correction inductance is there practically for free. So the current regulating CWA ends up with the similar cost, complexity and losses as a power factor corrected HX (an impedance equivatent for a series choke at 230V), the CWA became the standard for lamps that the constant current behavior suits.

HX ballasts are equivalent to a step up transformer and a choke. Both are linear components that don't change their behavior when the voltage varies :

The transformer will always convert the voltage by the same ratio, and higher input voltage will translate into proportionally higher output voltage

The choke is a linear component, it has some fixed impedance, and applying higher voltage to it will result in proportionally higher current



CWA have a magnetic circuit which is reaching a built-in physical limit in normal operation :

There is a part of the ballast core with precisely limited cross section area, which will allow up to a specific magnetic flux to go through and reach the secondary winding before it saturates. When it does, increasing induction in the primary winding (by increasing the voltage) won't be able to push any higher flux through the narrow part of the core, if the excess flux have somewhere else go to

An additional magnetic bridge (additional part of core), distanced by small air gaps from the main core, allows the excess flux to close around the primary winding alone, without affecting the secondary