The ai filters are not named like their tags.
https://itch.io/games/ai-assisted = https://itch.io/games/tag-ai-generated
https://itch.io/games/ai-graphics = https://itch.io/games/tag-ai-generated-graphics
The "assisted" appears on every project that has answered yes to the ai disclosure along with the selected categories. And as OP has pointed out, the assisted can be mistaken to mean something other than for example that ai assets were used for graphics. It's redundant, as it's meaning is only, that one or more of graphics, sound, text or code are selected. It has no other meaning. But assisted does imply other things.
If you click on the filters in the more information box, it will open a new browse filter selection on the left side, just like released / in development. Or the platform filter.
But there is no formal way of entering the specifics about ai usage. Like ai made, hand edited. Or coloring done by ai. Just go browse Steam for some ai games to see how it looks on a big store.