Wish and the Ring of Spell Storing

Is it possible to use Wish to cast Conjure Minor Elementals (upcasted to level 5) into a Ring of Spell Storing? Or it counts as a level 9 spell no matter what?

Wish is the mightiest spell a mortal can cast. By simply speaking aloud, you can alter reality itself.

The basic use of this spell is to duplicate any other spell of level 8 or lower. If you use it this way, you don’t need to meet any requirements to cast that spell, including costly components. The spell simply takes effect.

RING OF SPELL STORING: This ring stores spells cast into it, holding them until the attuned wearer uses them. The ring can store up to 5 levels worth of spells at a time. When found, it contains 1d6 − 1 levels of stored spells chosen by the DM.

Any creature can cast a spell of level 1 through 5 into the ring by touching the ring as the spell is cast. The spell has no effect other than to be stored in the ring. If the ring can’t hold the spell, the spell is expended without effect. The level of the slot used to cast the spell determines how much space it uses.

While wearing this ring, you can cast any spell stored in it. The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster but is otherwise treated as if you cast the spell. The spell cast from the ring is no longer stored in it, freeing up space.

Its a 9th level spell no matter what you do with it

How about if you use the Genie Warlock subclass feature Limited Wish?

Limited Wish

You entreat your patron to grant you a small wish.

As an action, you can speak your desire to your Genie's Vessel, requesting the effect of one spell that is 6th level or lower and has a casting time of 1 action. The spell can be from any class's spell list, and you don't need to meet the requirements in that spell, including costly components: the spell simply takes effect as part of this action.

Once you use this feature, you can't use it again until you finish 1d4 long rests.

It says that the spell "simply takes effect" but does it count as it having been cast?

Both Wish and Limited Wish are duplicating the effect of another spell, but not actually casting it. Technically, a Ring of Spell Storing requires you to actually cast the spell.

That said, some DMs might well allow it, and even if they didn't it could certainly fall under the "reshape reality" usage of Wish, with all the downsides that entails.

But why would you want to do that instead of just casting Conjure Minor Elementals into the item directly?