[2022] When does Spell Suppression happen in the damage calculation

Note that armor uses the initial_hit, not the mitigated_hit.

This is not true and never has been. Any other form of mitigation, such as resistances, that's applied before armour will change how armour interacts with that damage. It does not use the "initial" or unmitigated damage for calculating physical damage reduction.

Often nothing else will mitigate physical damage before armour, so this makes no difference, but it absolutely does not look at some "initial" value that can be different from the value with previous mitigation factored in.

Suppressing damage, however, happens after armour because it's a modifier to damage taken.

You cannot, but not because they're exclusive, because suppression happens fist.

Damage is suppressed, then stun is calculated, then the remaining damage can be blocked (fully, or partially with something like Glancing Blows)

Additional sources of "reduced -x- damage taken" are applied additively to the effect of Armour.

Not quite - you are confusing "[type] Damage Reduction" with "reduced [type] Damage taken" (which you had already correctly stated applies after armour, as a modifier to damage taken).

Armour applies "Damage Reduction" to the damage types it mitigates - usually this is physical, so "Physical Damage Reduction" Other sources of additional "Physical Damage Reduction" are additive with the Physical Damage Reduction calculated from armour. I don't believe there are currently any modifiers granting "additional [type] Damage Reduction" for types other than physical, but they would add to any damage reduction to that type provided by armour (if any - or add to 0 if armour doesn't apply to that type). Armour doesn't mitigate damage over time, but "Damage Reduction" does, so sources of additional Physical Damage Reduction mitigate physical damage over time.

"reduced [type] damage taken" is just a generic modifier to "damage taken" - which is inhernetly the post-mitigation value. All things modifying "damage taken", be they less/reduced/more/increased/-/+ apply after resistances & armour.

Yes, the terminology between "reduced damage taken" and "damage reduction" is unfortunately similar. Internal efforts to try to rename "damage reduction" to something else have so far not worked out for various reasons.

It hasn't been asked yet but I suspect someone will bring this up now I've talked about armour applying to things other than physical - in cases where armour mitigates multiple types of damage, it does so separately for each type it mitigates. If you make armour apply to lightning damage as well as physical damage, then take a hit containing both physical and lightning damage, then armour will calculate Physical Damage Reduction based on comparing the physical damage to armour, and apply that only to the physical damage, and will calculate Lightning Damage Reduction based on comparing the lightning damage to armour, and apply that only to the lightning damage.

100%. Trancendence just has the boolean property that armour applies to that damage, saying that 8% of armour applies is effectively redundant - that 8% was already applying, as was the rest of it.

Modifiers which allow you to take damage of one type as a different type instead apply pre-mitigation. They wouldn't really do much otherwise.

Those aren't a modifier to damage taken, they're changing the process of how you take damage, which includes mitigating it in all forms.