There are so many ways tyres can affect aero I think even experts struggle to consider them all.
As I am at a loose end, I thought I would post here, not with the intention of stating 'this is what happens' because I am no expert, but as a sounding for us mere mortals to chew it over.
Some of what I say will be just my interpretation of it, or even plain misconception, so please correct anything yo have issues with, but in a fashion that adds to the discussion, not just 'you are talking crap'. 'You are talking crap because.... ' is fine though
The bits I will try to add.
Tyres affect ride height, which affects handling. The 'softness' of the tyre wall governs how far the center of the hub, and so the floor of the car is above the track. A stiff wall will not deform much when downforce loads the car a soft one will. (ride height changes at speed=affects aero etc)
The rolling radius of the tyre also affects height, and the amount of material that gets removed during its use lowers the car by that same amount. If it is 10mm, a car with a worn tyre is 10mm lower etc.(doubt it is that much though)
The sidewalls flex when the car corners or rides a curb. This in effect puts the rubber in a different place to where it was on the straight. only a tiny amount, but possibly enough to be noticed by aero. A softer wall also allows the centrifugal effect to deflect the tread area too, so it works both ways.
The profile of the tyre affects airflow around it and the car, as to a smaller extent does the texture of it. The tyre is spinning so texture affects the airflow coning off it and reflected by it.
The engineers calculate what they call 'Squish' which is like the air you feel if you clap your hands infront of your face. They try to direct this to their advantage. The profile affects this too
There are several more effects but I couldn't even begin to explain them, so hopefully some one with more knowledge will assist, and straighten out some of the rubbish I have posted.
Keep it civil and we could learn stuff (it wont hurt, it may even be handy