The series in 2021-22 resulted in a 2-1 win for South Africa, after India won the first Test. India has failed to win a Test series in SA, although they have won at least one series in all other countries. The best India has done there is an 1-1 draw in 2010-11. The 2021-22 series followed the pattern of 2006-07 where India won the first Test but lost the next two.
Here is an overall summary of Tests between these two countries:

SA leads India 17-15 overall. Both sides appear to have strong home advantages.
We now look at individual performances, starting with
Batting:
Most runs (500 or more):

Led by Tendulkar and Kallis.
These two have the most centuries (7)
Amla, Kallis and Tendulkar have the most 50+ scores (12).
From the above table, the best by current players is 1236 by Kohli, followed by Rahane, Pujara and Elgar with 800+. RG Sharma is further down.
Highest innings (125 or more):

The highest by current players are 254* by Kohli, followed by double centuries by MA Agarwal and RG Sharma. But no one crossed 125 in this series.
Highest batting averages (Minimum 20 innings, all instances):

Kallis has the highest average, followed by Kohli at some distance. Other current players here are Rahane, Elgar and Pujara.
Highest strike rates (Minimum 1000 balls faced, all instances):

Sehwag and Azharuddin lead here. Among current players there are RG Sharma (in 3rd place), Kohli and Rahane. Also note Dravid at the bottom of this list.
Bowling performances:
Most wickets (12 or more):

Led Kumble, followed by Steyn and Srinath at a distance. Ashwin (56) has the most by a current player, followed by Shami, Rabada and Jadeja. Also note M Jansen with 19 in his debut series.
The most 5-fors are 5 by Steyn and Ashwin. No one has taken more than one 10-for.
Best innings bowling (includes all 6wi and more):

The best performance was an 8-for by Klusener on his debut.
Current players here include SN Thakur, Ashwin and Ngidi.
Thakur’s 7-61 in this series is the best for India against SA, surpassing the earlier record of 7-66 by Ashwin (Nagpur, 2015) and 7-120 by Harbhajan (Cape Town, 2011) which was India’s best in SA.
Best match performances (includes all 8wm and more):

Led by Ashwin and Donald with 12-fors, and 10-fors by Steyn, Pollock and V Prasad.
Current players here include Ashwin, Jadeja and Ngidi.
Best bowling averages (Minimum 2000 balls bowled, all instances):

Headed by Donald and Jadeja (!) Current players here include Jadeja, Shami, Ashwin and Rabada.
The best economy rates are by Pollock and Jadeja.
The best strike rates are by Steyn and Shami.
To be continued.