Preface: I hope for an equally, if not more, instructive answer like this for 'be-'.
[for-:] prefix usually meaning "away, opposite, completely,"
from Old English for-,  indicating loss or destruction,  but in other cases completion,
and used as well with intensive or  pejorative force,
from Proto-Germanic * fur "before, in" (cognates [...]);
from PIE * pr-, from root * per- (1)  "forward, through" (see per).
In verbs the prefix denotes (a) intensive or completive action or process, or (b) action that miscarries, turns out for the worse, results in failure, or produces adverse or opposite results. In many verbs the prefix exhibits both meanings, and the verbs frequently have secondary and figurative meanings or are synonymous with the simplex. [Middle English Dictionary]
Probably originally in Germanic with a sense of  "forward, forth," but it spun out complex sense developments in the historical languages. [...] Ultimately from the same root as fore (adv.). [...]
I am guessing that forwardness to act, implies interest and willingness to act, which can inspire (a). Please advise whether this previous sentence seems to explain how  evolved to mean  and (a).
But how might have  evolved to mean (b) ( which Etymonline divides into  and  )?
What shifted semantically?