'provide Ukraine with' is best
Here are two alternative, normal-speech English versions of the longer phrase:
...the capabilities we're providing Ukraine with
...given we're providing Ukraine with these capabilities
This second example above shows what
with would mean. While
with is a preposition, prepositions can be used by themselves if the noun they accompany is unknown in a somewhat re-arranged sentence, meaning something like this...
We're providing Ukraine with capabilities and have been evolving the capabilities we’re providing Ukraine with.
In that example,
with somewhat points to the previous
with. Because we already know this, we don't need the part of the sentence before
and in order for this to work. Hence
providing Ukraine with is best.
This would use
...the capabilities we're providing to Ukraine
to would both come from the Dative Noun Case, if translating from Russian, Greek, German, Czech, et cetera. In English, the two prepositions are similar and often exchangeable, though not identical. So, the speech pattern from John Kirby might indicate a "speaking mistake made by someone with advanced English skill". If he was typing it out, he might have likely used
providing Ukraine with.
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