I think limited slip differential is rather different to TCS.
TCS is like ABS in reverse, monitoring the rotational acceleration of the wheels, then braking or backing-off the throttle to regain grip.
Whereas limited slip differential monitors and allows a certain degree of difference in left and right drive shaft rotations.
A good example would be to imagine a car driving with one wheel on tarmac and the other in wet mud.
TCS would back off the power until the wheel with less grip regained grip.
LSD can allow for the same power to be transmitted, but with more of the power going to the wheel on the tarmac.
Or as often seen on Top Gear, a car going quickly around a corner
A car with no LSD and no TCS will have a smoking inside tyre due the power being delivered to the inside tyre that lacks grip
A car with TCS will brake the inside wheel or reduce power (depending on TCS type)
A car with LSD will remain on power and if pushed harder will give a satisfying power slide J
I think if you want a car with TCS then it’s easier to buy a car with one originally installed rather than retro fit it.
In my opinion car with LSD but no TCS when pushed will get you into trouble……power slide…….then spin.