on the left: marking which of two matching things, a hand, a side, or a pillar, is the left one
This is a labeling word. It says nothing about being left-handed, and nothing about skill, weakness, or luck. It simply picks out which of two matching things is the one on the left, and it does that job in only nine verses. In six of them its partner on the right (יְמָנִי) is standing in the same sentence: the right finger and the left palm, the right pillar and the left pillar, the right end of the temple and the left end.
Its uses gather in two settings. In the ceremony for cleansing someone who had recovered from a skin disease, the priest pours oil into his own left palm and dips his right finger into it, so the left hand is the hand that holds while the right hand works. In the descriptions of Solomon's temple it tags the left pillar, the one named Boaz, and the left end of the building where the guards were posted. Only in Ezekiel does it step outside those two settings, where the prophet is told to lie on his left side.
Because an Israelite got his bearings facing the sunrise, the left hand pointed north, and the noun this word is built on (שְׂמֹאל) can mean north all by itself. The temple faced east, so its left side really was its north side, and several English Bibles print "north" outright in those verses. The word itself still says "left", and when the text wants to name the compass direction plainly it has an ordinary word for it (צָפוֹן).