The irregular superlative adverb or adjective of ‘far‘ is ‘farthest‘ or ‘furthest.’
If I take one more step, it’ll be the farthest away from home I’ve ever been.
From the furthest corners of the world where the dark arts still hold sway,
he returns to us to demonstrate how nature‘s laws may be bent.
In the English Vocabulary Profile, at A2, ‘far‘ as an adverb means:
at, to or from a great distance in space or time
It is also listed at B2 as an adjective in the attributive position:
describes the part of something that is most distant from the centre or from you
From a search in the iWeb corpus for farthest|furthest
1 FURTHEST (JJT) 11156
2 FARTHEST (JJT) 9976
3 FURTHEST (RRT) 4226
6 FARTHEST (RRT) 3230
We can see that the adjective form is more common than the adverb form and that ‘further‘ is a bit more common.