At the start of the 2nd Test between England and South Africa at Manchester, it was mentioned that JM Anderson was the first to play 100 Tests at home.
This is true. Let us also look who has played the most Tests overall, away and neutral.
These figures include all those playing in the Manchester Test of 2022, and do not include the ICC XI v Aus Test of 2005.
Most Tests (125 or more):

Tendulkar (200) is followed by Anderson (174) and SR Waugh (168). The next from India is Dravid (163).
Also: Anderson (174), Broad (158), Warne (144) and VVS Laxman (134) have played the most Tests without ever captaining their sides.
Most Tests at home (60 or more):

Anderson leads with 100, followed closely by Tendulkar (94), Broad and Ponting (91 each). the next from India is again Dravid (70).
Most Tests away (other than neutral venues), 60 or more.

Tendulkar leads with 106, followed by Dravid with 93. Next is Chanderpaul with 81. Ponting, Anderson and Broad are further down.
And finally,
Most Tests at neutral venues (7 or more):

As you may guess, Pakistani players dominate this list starting with Asad Shafiq (30), Azhar Ali (29) and Younis Khan (28).
The highest by a non-Pakistani player is 8 by R Herath, followed by several others with 7. These include some NZ players who played in the WTC final against India in England in 2021.