I think it would have been incredibly harsh to penalize that and, as you note, against the spirit of the laws. What advantage did Arsenal gain by Gabriel handling the ball?

The whistle is the whistle - the start of it indicates that play may start. The play had clearly restarted here. Letter of the law, it IS a penalty.

If Kane or another Bayern player had immediately gone into the penalty area and pressured before it was picked back up, the referee would have likely had a much, much more difficult decision to make. Because it goes from trifling/common sense no foul to mattering