Does the 'Fiery Soul Trap' enchantment's Soul Trap effect work properly on certain enchant-able weapons with unique properties?
Solution 1:
Turns out this was caused by a mod. Spell Sneak Attacks, in my case.
The 'Fiery Soul Trap' enchantment's Soul Trap effect work properly on weapons with unique properties like The Longhammer and the Silver Greatsword, in vanilla, no-mod Skyrim.