First let me state, again, that proverbs are notoriously difficult to translate; sometimes more difficult that poetry. This is often because they are deliberately vague so as to maximize their application. All languages do this by exploiting grammatical loopholes and semantic double meanings.
In the case of Prov 22:19, we have a single verse that is part of a larger section, usually (but not uniformly) designated as Prov 22:17-21 being a combined introduction to the 30 sayings of the wise and the first of these 30 sayings.
The OP asks about the literary function of the last two Hebrew words, "even you", or, "indeed you", "yes, you", etc. The answer is tersely summarized by Barnes:
Even to thee - The wide general character of the teaching does not hinder its being a personal message to everyone who reads it.
Thus, these final two words are added for emphasis that these proverbs definitely apply to each and every reader.