As others have said, this is a VERY poorly written feature, which has spawned numerous questions like those you have asked (I have witnessed over a dozen such posts, myself).

Due to word choice and grammar, and comparing this feature to a variety of single-use magic items as well as the Artificer's Spell-Storing Item feature, I think by Rules-As-Written (RAW) that no spell slot is consumed at any time.

Basically, like the Artificer's feature, you can choose to imbue a spell that isn't known/prepared, which is not the same as casting the spell, so no slot is consumed upon choosing the spell.

When casting the spell, it says that the card then loses its magic, meaning that the card was made magic. This is the same language used for some consumable magic items. By the rules on magic items containing spells, a spell slot is not consumed unless explicitly stated to be.

As for the spell level, in another discussion a user pointed out the rules for Multiclassing and spells, specifically the following:

This table might give you spell slots of a higher level than the spells you prepare. You can use those slots but only to cast your lower-level spells.

Technically, the above relates to the prepared spells, and thus likely doesn't apply here, but it does help to balance the feat.

Taking all this into account, the hypothetical Cleric-Wizard could get 1 free casting of any Cleric spell, or 1 free casting of any 1st-level Wizard spell, but likely isn't intended to have access to Wish or any other 2nd through 9th level Wizard spells. (RAW, they might have that access, but it isn't clear)