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Solvent leveling means that strong acids completely dissociate in that solvent so it is impossible to distinguish between two acids that completely dissociate in it. A solvent levels and acid if the $K_\text{a}$ of that acid is greater than 1. However, that’s not completely dissociated. An acid can have a $K_\text{a}$ of 2, 3 or 25 what’s the problem with being able to distinguish between them? In truth, whatever the $K_\text{a}$ it’s not actually COMPLETELY dissociated.

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Your final statement:

in truth, whatever the $K_a$ it's not actually COMPLETELY dissociated

is exactly right.

Strong acid is very often stated to be "completely dissociated", but that's just wrong.

For example, nitric acid has a $K_a$ of 24, so 1M nitric acid about 96% dissociated. If the concentration is higher, it will be less dissociated and if the concentration is lower it will be more dissociated.

I would think of the solvent leveling effect this way:

Suppose you have 1 liter of 0.1M ethanol in water and you add 0.1 moles of sodium amide thinking that it will deprotonate the ethanol. That's not going to happen because most of the protons that protonate the amide will come from the solvent (water) rather than the ethanol.

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