Hears my personal analysis:
An enchanted item is the embodiment of casting a specific spell, with all parameters fixed at creation.
A practitioner, as a distinct spell, can extend one of their own Evocations (and presumably refresh the duration of a Thaumaturgical spell) if that Evocation has not yet ended (including if it would end at the end of their turn).
When dealing with a spell created via an enchanted item, for many purposes, the enchanted item is the caster of the spell.
The practitioner wanting to extend it isn't the caster, and so can't extend it directly.
The enchanted item can only cast a singular fixed spell per slot.
Therefore, the only way to extend an enchanted items spell is by using a two slot enchanted item, with one slot being the base spell and the other spell being the extension of the first spell.
YMMV, if I were actually running a game, I'd likely let someone capable of reliably casting the spell from an enchanted item they made extend it.