Learn English – “provided by” vs “provided with”

The preposition within has nothing to do with the ordinary sense of the preposition with = “accompanying, alongside, by means of, etc.”. Within means “inside” in spatial, temporal and figurative senses.

The hoard was discovered deep within the mound.
You must respond to this communication within thirty days.
They are within their rights in refusing to be interviewed.

Consequently, within is not a valid translation of German in in this context. However, English does support both German uses: you may use either with for mit or in for in.

With this option ...
In this option ...

• HISTORICAL NOTE, for those who wonder why the compound with + in has this meaning:

  Old English wið (cognate with German wider) originally meant “against, by, back from”, and the modern sense of with was expressed by mid (cognate with German mit). In the later part of the Old English period, however, northeast England was occupied and to some extent settled by speakers of Old Norse dialects, and over the next centuries (down into the Middle English period) many Old Norse words replaced the corresponding Old English words. For instance, they and are are of ON origin. Old Norse við, a cognate of with and wider, had approximately the sense of mid and mit, and under its influence, with shifted to the modern sense. However, the old sense lingered in established compounds such as withstand (stand against), withhold (hold from), withdraw (draw away from)—and within (against or by the inside).

Somebody^Subject provides somebody^{IndirectObject} something^DirectObject.
Somebody^Subject provides somebody^DirectObject [_{PrepositionPhrase} with something].

The two forms are exact equivalents, they are both current and idiomatic in all registers, and there is no reason to prefer one to the other in any context.

The double forms arose because at one time provide was often used in the sense equip, taking the entity supplied as its DirectObject: one spoke of providing an army or ship, meaning to supply it with whatever it needed. In this case, PrepositionPhrase was needed to specify what “provisions” were supplied.