to stand against someone as their adversary, whether by open hostility or by bringing a charge against them
This word describes taking up a position against a person. It is not a private feeling of dislike but something done out in the open, and in every one of its six uses the target knows he is being stood against. The noun built from it, the word for an adversary (שָׂטָן), names the person who does this; this verb names the doing of it.
The six places it appears fall into two settings. In two psalms the opposition is plain enmity: people repay the speaker's kindness with harm and hunt him down. In the other four the setting is a court. Psalm 109 asks that an adversary be posted at the accused man's right hand, the spot where a prosecutor stood, and the same picture appears in Zechariah 3, where a figure stands at the right hand of the high priest to press a charge against him and God overrules the charge.
That courtroom scene is where the later idea of Satan starts, but the later idea is not yet here. In five of the six verses the ones doing the opposing are human enemies of the person praying. In Zechariah the accuser is a member of God's own court carrying out a role inside it, and he loses the case.