A tyre generates greater slip angles when it is new and its' tread blocks are deepest, and smaller slip angles as the tread blocks wear down. The tread blocks distort, they move sideways and twist with the lateral and axial steering forces imparted into the blocks. They do this more the deeper the blocks are, the smaller area of the blocks, and also the softer the tread rubber is. The more the tread blocks 'squirm' under lateral load the greater the difference between the direction in which the wheel is pointing and the orientation of the tread rubber at the road / tyre interface. As the tyre wears down this difference decreases, so the tread face has an increasingly greater fidelity with the direction in which the wheel is pointing.
This is at least one reason why higher 'performance' tyres tend to have larger tread blocks (greater distance between tread grooves and fewer grooves), and often shallower grooves. The larger shallower blocks tend to 'squirm' less than smaller deeper blocks, especially with the softer rubber used in 'high performance' tyres. And, at least one reason why dry weather racing tyres have no tread grooves (or only vestigial ones).
So all else being equal, newer tyres (that generate larger slip angles) fitted on the rear of the car (with somewhat worn tyres fitted on the front) will encourage oversteer, more so the greater the lateral forces acting on the treads. Fitted to the front (with somewhat worn tyres fitted on the rear), they will generate understeer.
Personally, over the years a number of times I have fitted new tyres to the rear of a number of different cars (with more worn tyres on the front), and each time I did not like the result much. The back end would feel 'vague' and 'wooly' compared to the front end, especially as cornering forces increase. Understeer decreased, but not in a nice way. The rear end isn't all that stable with full depth tread on the rear tyres (and less depth on the front tyres, maybe 1/2 depth, or so, give or take).
I recall one occasion when the then current car had newish tyres fitted on the rear only (enough kms to be scrubbed in, but still effectively full depth treads). I was attacking one of my favourite corners no harder than I had easily done many many times before, and the rear end just lost grip, badly. The car travelled a long distance at least 45° to the direction of travel, a really big opposite lock slide, requiring huge skill to save (or maybe it was huge luck...).
Swapping the new tyres from the rear to the front certainly feels better to me. The steering and handling is more stable. I've tried this experiment a few times over the years, and the result has always been the same, the car was better with the new tyres on the front. These days I just put the new tyres on the front straight away, and the more worn pair on the rear.
However, I don't like new tyres much. I can feel the blocks moving, the steering becomes vaguer and handling diminishes compared to part worn tyres. I like my tyres best just as they are in need of replacement due to lack of tread depth. At minimal tread depth I find that tyres are more precise, steer better, handle more 'solidly' and are more consistent.
Where new tyres are probably better is in rubber hardness, because rubber get harder with age and heat cycles. So for me, all else being equal the best tyre is a new one that has had most of its' tread shaved off, though not a practical nor economic option...