As others have already pointed out, Barkov has been better than Bobrovsky during the whole run. Bob has had one elite game, the first game of the finals, but then again Barkov has played against McDavid and Draisaitl and even then Barkov has created one and score one game-winning goal during three finals wins thus far. I wouldn't say Bobrovsky has been clearly better of the two during the finals, let alone the whole playoffs.
When you look at goals saved above exptected, Bobrovsky has been the third best goalie these playoffs after Swayman and Shesterkin and worse than he was last playoffs. That doesn't mean he has been bad, just that the team hasn't required him to stand on his head like last year except for the one game. Overall Bob has been solid, above average winning goalie these playoffs.
Barkov on the other hand leads Panthers in points and is a Selke level defensive forward. On top of that, his contribution to game-winning goals has been great these playoffs with 3+4 points on GWGs in 15 wins.
In my mind, it definitely should be Barkov and it's unfathomable that Bobrovsky is so much ahead of him in bookmakers' odds. But as with other NHL awards, the Conn Smythe is prone to recency bias and media storylines.