There is an "it factor" when it comes to consistent playoff performers, no luck involved. Every now and again a guy can have a one off great playoff, like Keith Primeau in '04, but the best playoff players perform nearly every postseason regardless of circumstances. Doug Gilmour was great in the postseason from his rookie season till the day he retired. O'Reilly is a current one, who's performed in the playoffs nearly every time he's made it. I suppose a player would need to be lucky to be on a winning team that makes the playoffs, but once you've shown aptitude on the highest stage your services are always inquired about.
There's also no style that automatically translates. There are power forwards that you'd think could translate given their propensity for goal scoring and violence, but then you see guys like the aforementioned Keith Tkachuk or Todd Bertuzzi just flop in the playoffs. Meanwhile a skilled but soft and one way winger in Phil Kessel scored consistently and at a high level in the playoffs during his youth and prime.
I think there's a level of fearlessness that you need to have to succeed in the playoffs. Not just not being scared of big and tough teams and being able to play through it and give it back, but not being afraid of making a mistake and overthinking things. Mitch Marner's over the glass penalty in Game 6 of 2021 is a prime example of this, guy had all the time in the world to ice it and yet he chucked it into the stands, clear case of a guy in his own head afraid to make a mistake. Also can't be afraid of throwing your body into the path of a shot puck, taking a hit to make a play, just generally stepping out of your comfort zone.
So much pressure in the playoffs, need to have a certain personality to adapt and thrive. Some guys can take that anxiety and use it as fuel to elevate themselves, other guys are cool as cucumbers and don't let the pressure throw them off from their usual regular season dominance.
I'm trying to think of defensemen this phenomenon applies to. Lot's of forwards that choke in the playoffs after dominant regular seasons, can't think of too many defensemen that turn into flops come playoff time. I guess Jake Gardiner is an example, could skate like the wind and was great offensively, but come playoff time he got in his own head and was mistake prone, Bruins ate him alive in '18 and '19. Defensive defensemen that have good regular season results don't often seem to flop in the playoffs. Maybe that's due to expectations or big defensive defenseman is truly the safest play style that translates.