Partial Frame Challenge
Individual left on base is a meaningless statistic that is reported virtually nowhere that has a meaningful statistical background. MLB.com does report it in their box scores, but no other major site that I could find even reports any LOB beyond Team LOB, nor do the newspaper box scores of old that I could find. Fangraphs does not list it, and Baseball-Reference neither lists it nor even allows you to search for it (in their Stathead system). While I don't have specific evidence for this (as it's so fully ignored there's no way to prove this negative), it clearly has no predictive value - as baseball is the leading sports in advanced statistics, and this isn't even available to look at without reconstructing it yourself.
Further, the MLB official scorer handbook does not list individual left on base as a statistic the scorer is expected to keep. As a result, I would define this term as "unofficial" and attribute no specific definition to it; it is something each site/person may define for themselves.
That said, it is possible to determine some of the rules that MLB.com follows by inspecting box scores and the play by play for those games. For example, in the game between the Detroit Tigers and the Chicago White Sox on 10/3/2021, Akil Badoo is listed as having 2 LOB. He left two runners on base in the third inning (when he popped out), and then later had a sacrifice fly to score a run with two on in the ninth inning. The final score has him with 2 LOB, so clearly a SF does not count against LOB (even the runners who weren't scored).
Further, in a game the same day down I-55, the Cubs and the Cardinals played, and the Cardinals pitcher had a sacrifice hit in two plate appearances, and 0 LOB. As such, he had zero LOB.
So clearly, neither kind of sacrifice is counted as any LOB by mlb.com.
As far as double plays, they do count as LOB (the runner who was also out). Look at Sosa (not Sammy, but Cardinals shortstop Edmundo Sosa); he had 3 LOB, grounded into a double play with two on, one of whom scored, in the second, and then grounded into a fielder's choice in the fourth with two on. Every runner who was on and didn't score was counted against him, even the runner who was doubled off and the runner who was put out on the fielder's choice.
And, as far as errors, Tigers first baseman Harold Castro (not catcher Willi) in the game above reached on an error by White Sox third baseman Yoán Moncada, with one runner on. That was the only "out" he (should have) recorded that game with a runner on who did not score (he also had an earlier sacrifice fly, but we determined that does not count separately, and there were no runners left on in either case). As such, he was clearly credited with an LOB for it despite reaching safely.
So to wrap up: SF, SH do not count any LOBs. GIDP counts the doubled-off runner as an LOB. E counts as an out (as it does elsewhere). Most likely, MLB.com simply counts any runner on base at the start of an at bat who had not scored by the end of the at bat, where the batter received an at bat but did not record a hit.