Another factor to consider is weight.
Larger rims weigh more than the OE 13” rims, heavier rims affect acceleration, braking, handling, ride and by extension economy (which none of us care about
) Greater inertia due to weight is the culprit here. More load to manage by the shocks and springs as the tire bounces up after going over a road imperfection, keeping the tire in touch with the road is what is important.
There is a limit to the value of adding tread width on a light car, you get to a point of diminishing returns quickly. The biggest value from a performance perspective of going to a 15” tire/rim combo is the reduced reaction time/stiffness of the shorter sidewall, at least on track or autocross. Modern cars need more tread width as they are dealing with much more weight, a GTI in 1983 was just over 2100lbs, today they are over well over 3100lbs.
I would use a tire/rim calculator to map out what is possible without major changes but as Ulix points out, diameter is going to be the limiting factor. Old cars had smaller wheel openings and wheel houses with an intended relationship of the wheel/tire assembly to the strut assembly. With coil overs you will gain vertical space potentially but you will run out of wheel opening. With a larger overall diameter you will change the final drive of the car making it in effect ‘taller’ which will negatively affect acceleration even more (larger circumference, more weight to turn equals poorer acceleration).
I have included a PDF from one of the many calculators out there which gives a very good summation of wheel/tire setups.