ujm:
You wrote: “Is this pasuk missing from your Tanach (Mishlei 13:24)?: חוֹשֵֹ֣ךְ שִׁ֖בְטוֹ שׂוֹנֵ֣א בְנ֑וֹ וְ֜אֹהֲב֗וֹ שִֽׁחֲר֥וֹ מוּסָֽר:
It is outstanding. What is tragic is that you misinterpret it. I suggest you visit the writings of Rav Shlomo Wolbe ZT”L. He writes this in the Alei Shur. It is also found in the sefer Zriyah Ubinyan Bechinuch – a short sefer that is actuakky an excerpt of a few of his maamorim on chinuch. The use of שבטו is as a last resort, and that is why Shlomo Hamelech stated this in this manner. He never outrightly instructed to hit children. Chazal explain that this is not punishment, as use of a strap that causes pain is prohibited. Rather, a shoelace is used so it relays a messdage without punishing.
Next, your Shulchan Aruch seems to be precisely like mine. It doesn’t say to hit your child. It emphasizes that during the three weeks, one should not even potch when it is the appropriate thing to do. You then continue to expound on the limited use of petch, a point that I have made persistently. Yes, a potch has its place (well, you know what I mean). But too many here consider giving that potch as obligatory as davening three times a day. That is not at all what the Torah says anywhere.
Your last paragraph provides further support to my position. One must be completely cognizant of the result of giving the potch. If it is educationally productive, it is okay. If it produces resistance, traumatizes, injures, etc., it is forbidden. Again, there are times when behavior control is the immediate goal. I postulate that this is a tiny fraction of what we need to be doing as parents and mechanchim.