Answer

In Rashi and in Shittah Lo Nod'a LeMi there, they explained that it says "he shall send him free" instead of "he is free." The extra verb comes to include many acts of sending free. The later authorities (see, for example, Atzmot Yosef) objected that seemingly these words of Rashi refer to what follows, where multiple forms of emancipation are included, and not here. But in my opinion they are mistaken, and Rashi really does mean it here. And what troubled him was precisely your question. Therefore he writes that the inclusion implied by "sending free" comes to teach that there is a general term at the end here. (True, this is not really an inclusion of multiple sendings, but the phrase of sending is what broadens. And that is the difference between the two derashot: whether one includes multiple forms of sending free, or whether one broadens the last specific term and turns it into a general term.)
There is here something like an "if it is not needed for its own matter" move, since this inclusion is not understandable (according to the derashah here; the derashah later indeed finds another solution for it, and then in fact they do not expound it as general and specific and general). Therefore they redirect it into serving as a general term for the preceding structure.
A tentative scholarly note: it seems to me that the earlier cases of general and specific were careful to use general and specific according to the content itself (as in "herd and flock, wine and strong drink, and whatever your soul desires," regarding redeeming the second tithe), but in later generations these derashot were expanded and general terms of more indirect kinds were introduced. And perhaps in these indirect derashot the intention is only as a scriptural support, but this requires further investigation.